







4^x=2^x+6 
20190405 

From Olivia: How do you find the (b,n) if the solution of the equation 4^x=2^x+6 can be expressed at logb(n) where b and n are both prime numbers? Answered by Penny Nom. 





Double the number of pennies each week 
20190228 

From Donald: If I save a penny a week,double it every week,How many weeks will it take to reach 1,000,000 dollars Answered by Penny Nom. 





y=lnx+(1+ln2)/2 and y=x^2 
20190128 

From Mike: Prove that y=lnx+(1+ln2)/2 and y=x^2 touch each other.
The course is about logarithm and root functions... how should I solve this problem? Answered by Penny Nom. 





4444^4444 
20171210 

From Sashi: 4444 to power of 4444=?
Please share the result with simplification. Answered by Penny Nom. 





The derivative of f(x)=2^x/x 
20171128 

From Chhavi: f(x)=2^x/x.
Find f'(x). Answered by Penny Nom. 





3^2x5=27 
20161214 

From danaja: solve for the following 3^2x5=27 Answered by Penny Nom. 





Find two values of x satisfying f(x)=1 where f(x)=sin(ln(x)) 
20160121 

From Ruth: I'm trying to find two values of x satisfying f(x)=1 where f(x)=sin(ln(x)) Answered by Penny Nom. 





Manipulating an expression using logarithms 
20150518 

From Katie: Solve x=At^be^ct for b in terms of c.
The e is Euler's number, not a letter or random placeholder. v
I've tried 2 methods on my calculator, and I am unsure as to why they give me different answers, and which one is correct.
For some reason, when placing a multiplication sign in between the A and the first t, I get a completely different answer. Why is this?
Also, which is the right answer for the question I have?
Thank you!
Katie :) Answered by Penny Nom. 





logbase4 (sin x) = 0.5 
20141026 

From Susan: Solve for x: logbase4 (sin x) = 0.5 Answered by Penny Nom. 





Logarithms 
20140828 

From effaryna: how logarithms is applied in everyday life? Answered by Penny Nom. 





Differentiate ln[x(2x4)^1/2] 
20140628 

From Igwe: If y=In[x(2x4)^1/2],find dy/dx at x=3 Answered by Penny Nom. 





How do we use logarithms in our daily life 
20140601 

From ss: how do we use logarithms in our dailylife Answered by Penny Nom. 





Evaluate log3 14 
20131117 

From Tash: Use the Change of Base Formula and a calculator to evaluate the logarithm, correct to six decimal places. Use either natural or common logarithms.
log3 14 Answered by Penny Nom. 





4=(1+.08)^x 
20130615 

From Samantha: I can't seem to understand how to solve for x when it is in power form, here is the equation:
4=(1+.08)^x Answered by Penny Nom. 





How do i write log_8(P) =7 in exponential form? 
20130414 

From nancy: How do i write this in exponential form log8P =7 Answered by Penny Nom. 





Solve 8 logx > x 
20130219 

From Fulvio: Hi, could you solve this equation in algebraic form:
8logx>x Answered by Harley Weston. 





What is the domain of f(x)=sin(ln(x))/ln(x)? 
20130206 

From Behrooz: Hi, the following problem may be interesting:
What is the domain of f(x)=sin(ln(x))/ln(x)?
Be careful, domain is not obvious.
Best regards
Behrooz Answered by Penny Nom. 





The exponential form of log8=P 
20120425 

From Kristina: what is the exponential form of log8=P Answered by Penny Nom. 





A log equation in exponential form 
20111111 

From Sarah: Express the equation in Exponential form
log2 to the 16th power=4 Answered by Penny Nom. 





Uses of logarithms 
20111109 

From BEA: what is the use of logarithmic functions in real life or daily life? Answered by Penny Nom. 





Exponential form 
20110518 

From Kara: How do I write this in exponential form?
log 1/8 = 3 Answered by Penny Nom. 





ln(12 x) = 6 
20110303 

From Carolyn: solve the equation
ln12x = 6
Thank you
Carolyn Answered by Penny Nom. 





Daily life example of logarithms 
20110204 

From owais: what are the application or daily life example of logarithms? Answered by Harley Weston. 





Simplify the logarithmic expression 
20101202 

From Adori: Use the properties of logarithms to simplify the logarithmic expression. Log(1/250) base 5 Answered by Penny Nom. 





An equation involving logarithms 
20100927 

From mindy: Hi,
I am trying to find x, the equation is:
log_2(log x + 2 (log x)^(1/2) + 1)  2 log_4((log x)^(1/2) + 1) = 1
Thank you very much for your time. =) Answered by Harley Weston. 





y =  log(x) 
20100428 

From Alex: y=  log(x), where y = 4.3
solve for x. Answered by Harley Weston. 





Log[f(x)] 
20100308 

From sourabh: What is the number of solutions of the equation
9 x 2  18 x + 5 = 0 for x, such that the expression
log10[(x+1)(x+2)] exists? Answered by Harley Weston. 





Exponential form 
20090805 

From motaz: Let x = log_2 1/8 Write the exponential form of the equation and solve the equation for x Answered by Stephen La Rocque. 





Log_7 (4X) = Log_14 X 
20090708 

From Mukulu: Help me with this question because i tried my level best to get the right answer but i failed Log_7 (4X) = Log_14X Answered by Stephen La Rocque. 





(logx)squared + log (xcubed ) +2 =0 
20090519 

From michael: Solve for x: (logx)squared + log (xcubed ) +2 =0 Answered by Penny Nom. 





A property that decreases in value every year by 10 percent 
20090307 

From PEter: there is a competition problem where a cottage is worth 25000 years, but it decreases in value every year by 10 percent. Without a calculator, is there a way to find after how many years, the cottage will be worth 2500? (besides multiplying it out and besides logs) Answered by Stephen La Rocque. 





An inequality with logs 
20090306 

From Indrajit: (x/10)^(logx  2)<100..........how to solve this one?? Answered by Stephen La Rocque. 





If 5 to the power of y = 625, what is y? 
20090302 

From Charlene: If 5 to the power of y = 625, what is y? Answered by Penny Nom. 





A log base 2 problem 
20081126 

From dave: solve for x
(log base 2 of x)  (log base 2 of (x2)) = 3 Answered by Penny Nom. 





How do you solve "logx^4=4? 
20081117 

From Scott: How do you solve "logx^4=4"? Answered by Penny Nom. 





2^x = 1,000,000 
20080906 

From Peter: How do I solve for "x" in the following equation: "2 to the power of x = 1,000,000" ? Answered by Penny Nom. 





Solve e^x + e^(x+1) = 250 
20080825 

From Laura: "solve this equation correct to three decimals"
e^x + e^x+1= 250 Answered by Penny Nom. 





Write log_2 (1/8) = 3 in exponential form 
20080627 

From Jaime: how do you write log2 (1/8) = 3 in exponential form?
the 1/8 is a fraction and the 2 is a base of 2 Answered by Penny Nom. 





limit x>0 (logxlog(x1)) 
20080522 

From kritica: lt x>0 (logxlog(x1)) Answered by Harley Weston. 





Which is larger, 727464^512693 or 624610^518548? 
20080518 

From Yahweh: Lets say I have two very large numbers in the form of a^b:
727464^512693 and 624610^518548
I want to calculate which number is larger, but its unreasonable to type these numbers into a spreadsheet to get an answer right away. How could I determine the larger or the two numbers efficiently? Answered by Stephen La Rocque. 





The inverse of a function 
20080503 

From keith: please help me find the inverse of this function:
h(t) = 2 + 4 ln(15t) Answered by Stephen La Rocque. 





log2x+log(x+4)=1 
20080412 

From ryan: solve the equation for x, log2x+log(x+4)=1 Answered by Penny Nom. 





1(1P)^75=0.05 
20080405 

From Amy: 1(1P)^75=0.05 Answered by Stephen La Rocque and Penny Nom. 





ln (x)  x = ln (2) 
20071118 

From James: How do you make x the subject of
ln (x)  x = ln (2) Answered by Stephen La Rocque. 





Logs and exponentials 
20070731 

From Marsia: Explain how the functions of exponents and logarithms relate to each other. Answered by Penny Nom. 





log_{a} b + log_{b} a < 0 
20070708 

From Claire: Suppose a, b are real numbers taking all positive values except 1, determine (without the use of calculators) whether there exists values of a and b such that log_{a} b + log_{b} a < 0 Answered by Penny Nom. 





log(0.81) 
20070628 

From Ade: If log 3 = 0.477 . The answer of log 0.81 Answered by Harley Weston. 





Log base 2 of log base 2 of x 
20070627 

From alex: y = log base 2 of lag base 2 of x
The slope of the tangent to the given curve at its xintercept is..? Answered by Harley Weston. 





Understanding log equations 
20070510 

From Sean: The number, N, of people who have heard a rumor spread by mass media at time, t, in days is modelled by N (t) = a / 1+ be^ kt. If 50 people have heard the rumour initially and 300,000 people hear the rumour eventually, find a and b. If the rumour is initially spreading at the rate of 500 people per day, find k. Answered by Penny Nom. 





What is the limit of 3.x^(3/x) as x approaches +infinity? 
20070411 

From Teodora: What is the limit of 3.x^3/x as x approaches +infinity ? Answered by Haley Ess. 





A logarithm of a product and the product of logarithms 
20070227 

From Sharon: Can you please explain Explain the difference between a logarithm of a product and the product of logarithms and give examples of each? Answered by Stephen La Rocque and Penny Nom. 





A problem involving logs 
20061126 

From Beth: any help would be appreciated on how to solve without using the change of base formula for logarithms in the solution and check of the solution!!!
log256 (x) + log16 (x) + log4 (x) + log 2 (x) = 7/4 Answered by Stephen La Rocque and Penny Nom. 





How many digits are in the number 2^64? 
20060614 

From Trang: How many digits are in the number 2^{64}? Answered by Stephen La Rocque. 





An equation involving logarithms 
20060305 

From Chris: Given that log_{e} y = 0.3log_{e}x+1.2 show that y=3.32 x^{0.3}
Answered by Penny Nom. 





6^(x+1) = 12^(x3) 
20060205 

From BB: 6^{x+1} =12^{x3} Answered by Penny Nom. 





Differentiation, powers and logs 
20060106 

From Claudia:
Question: how do I find the derivative of
x* ln(x+(e^2))^2
x^lnx
x^(e^(x^2))
Answered by Penny Nom. 





cos x * cos 2x * cos 4x * cos 8x 
20050829 

From Leandro:
A = cos x * cos 2x * cos 4x * cos 8x
What's the value of log A at base 2?
Answered by Chris Fisher and Penny Nom. 





y = log(x) + x. Solve for x. 
20050826 

From Alain:
I have the following equation:
y = ln(x) + x
How do I solve for x?
Answered by Penny Nom. 





Extraneous solutions 
20050204 

From Heather: My teacher wants to know why there are extraneous solutions in logarithms? Answered by Penny Nom. 





Some logarithm problems 
20050127 

From Jo: Given ln x=7.1; ln y=8.2, Find ln(x^3y^7) Answered by Penny Nom. 





ln(hx+n) 
20050107 

From Anibal: if I have the eq.
y=hx+n
and I want to know ln(y), how do I process
ln(hx+n)? Answered by Penny Nom. 





Two problems 
20040802 

From JJ: A question on my homework assignment about logs says "suppose that x=logA and y=logB & write the expression in terms of x and y"
log(A  B)
Is this even possible? It seems like a typo.
Another is: "solve for t."
12(1.221)^t = t + 3
Is this one possible? If it is, I cant figure it out. Answered by Penny Nom. 





12(1.221)^t = t + 3 
20040714 

From Jay: This problem has me stumped since i cannot separate the t and the 3. Here it is:
12(1.221)^{t} = t + 3
It's on a logarithm worksheet, but how do i figure it out?! Answered by Harley Weston. 





(ln(50/x)) / (ln(40/x)) = a 
20040621 

From Un eleve: (ln(50/x)) / (ln(40/x)) = a = constante
comment extraire la variable x ??? Answered by Claude Tardif. 





Logs 
20040229 

From Sandy: find X
3/2logb41/2logb8+logb2=logbx
my book uses prop 7 to rewrite as
logb4raised3/2logb8raised2/3+logb2=logbx; then writes
logb8logb4+logb2=logbx how did it get here? Answered by Claude Tardif. 





A problem with logs 
20040222 

From Caitlyn: problem: ln x + ln (x2) = 1
I can solve this on the calculator, but the book wants 1+ [(sqroot)1+e]. How can I get the e? Answered by Penny Nom. 





Logarithms 
20040201 

From A student: Where did the word logarithmic come from? Where/whom did it originate? Answered by Harley Weston. 





Domain of a function 
20031014 

From Karim: Find the Domain of the Function H(x) = Log3 (4x + 7)10 H(x) = log base 3 times 4X plus 7 minus 10 i am having problem solving these kinds of problems. Answered by Penny Nom. 





Applications of logarithms 
20030916 

From A student: I have a project due in my algebra two class dealing with logs and where they are used in life, but I am having trouble finding websites that relate. So I would really appreciate it if you couldhelp me. Answered by Penny Nom. 





Natural logarithms 
20030722 

From Amanda: I'm going into my senior year of high school. I will be taking AP calculus, and my teacher gave us some homework over the summer. However, there are two things that I do not understand how to do. The first is, she wants us to be able to generate a unit circle by hand using 30, 60 and 90 degree triangles. I have used the unit circle in trigonometry, however I was never taught how to draw it. Secondly, I need to know how to do natural logarithms without a calculator. I was not taught how to do this, and the worksheet I was given only showed me how to complete them using a calculator. Answered by Claude Tardif. 





1996^1999 and 1999^1996 
20010729 

From Rajesh: what is greater 1999^{1997} or 1997^{1999}? Answered by Chris Fisher. 





Two log problems 
20010616 

From A student: Hi..this is one of 9th grade student in Fort Worth TX. well..I am doing EPGY stuffs in my school right now..and.. me and my teacher had problems to solve some advanced logarithmic thing. so I searched some sites to solve these two questions  (log base 7 * 10) * (log base 10 * X ) = 2
 log base 10 * (3x4) + log base 12 * X
 (log base 12 * 2) + (log base 12 * 5)
= log base 10 *4 Answered by Harley Weston. 





An integration problem 
20001130 

From A student: If a>0 and the integral from b to 0 of 1/(1+x) equals 1/2 the integral from a to 0 of 1/(1+x), express "b" in terms of "a" Answered by Claude tardif. 





Where will we use this in the real world? 
20001011 

From Jane Ann Musgrove: As a teacher of mathematics, I am always asked "Where will we use this in the real world?". I am seeking ideas/sites via the internet where students can find answers to this type of question. Can you help me? To be more specific, right now I am interested in finding careers where the employees would use the concepts of "Radicals", "Matrices", and "Logarithms". This information will be used by students to make presentations to the class on their findings from internet searches. Answered by Harley Weston. 





Logs and trig functions 
20000912 

From Becky: How do they get these answers?  log 8 + log 2 = ?
Answer is: log 16
 For 0 degree < x < 90 degree, how many solutions are there for the equation 2sin x = cos x?
Answer: 1
Answered by Penny Nom. 





Radioactive decay 
20000518 

From Catherine Sullivan: Please help me with the following: The radioactive isotope carbon14 is present in small quantities in all life forms, and it is constantly replenished until the organism dies, after which it decays to carbon12 at a rate proportional to the amount of C14 present, with a half life of 5730 years. Suppose C(t) is the amount of C14 at time t.  Find the value of the constant k in the differential equation: C'=kC
 In 1988 3 teams of scientists found that the Shroud of Turin, which was reputed to be the burial cloth of Jesus, contained 91% of the amount of C14 contained in freshly made cloth of the same material. How old is the Shroud according to the data?
Answered by Harley Weston. 





Two calculus problems 
20000501 

From Kaushal Shah: How Do WE Integrate the following Functions,  Integral xtanx dx
 How was natural base "e" discovered and why e=2.7.......
Answered by Claude Tardif. 





Logs 
20000412 

From Jessica: Write as a single log 3ln x  2ln(y+e) + 5ln(x12)  4ln y Answered by Harley Weston. 





Characteristic of a logarithm 
20000314 

From Andrew Strauss: What is the characteristic of log base 18 of 1980 ? Answered by Harley Weston. 





Logarithms 
20000118 

From Jennifer:
Hi I have a test tomorrow and I was wondering if you could help me with these two problems. Explain how to express y in terms of x if log3y=4log3(2X) The LN key on your scientific calculator is not working, but the ex and LOG keys are. Write directions for calculating a natural logarithm using the ex and LOG keys. Explain why these directions will get you the right answer. Answered by Harley Weston. 





Logarithms 
19991216 

From Pierre: Can you please answer those three question  inverse or the exponential function.
logx 81 = 4, x expo4 = 81, x = +or 4square root 81, x = +or 3 s.s = {3} Why is 3 not acceptable.  .
. . Answered by Harley Weston. 





Log Cancel 
19991203 

From Justin Murray: Ok I feel like a goof because I know this and I cant think of an answer But I want to isolate the x in the function y=2^x how do I do this? Answered by Harley Weston. 





Two derivatives 
19991116 

From Gina Renicker: The derivative of: y=e^{(xlnx)} and y=x^{2arctan(x1/2)} Answered by Harley Weston. 





Derivatives with logs 
19991026 

From Kate: What is the derivative of 5 to the 5x2 at x equals 0.8? Answered by Harley Weston. 





log(a) 
19991022 

From Brenda Miskimmin: I need to know the mercury concentration in mg/L or ng/L for the following: log M (Hg) = 8.5 where mw of Hg=200.59 (it's the negative sign in front of log that confuses me). Answered by Harley Weston. 





Solving using logs 
19991011 

From Rich Bolton: Here's my question: $541.39(1+i)^{15}=784.09 Can you please show me how to do this? Answered by Penny Nom. 





A log problem 
19990508 

From N. Lam: I don't understand how to do this type of question: log(base absolute value x)y = log(base abs.val.x)2 + log(base abs.val.x)(Cos x) How do you graph the equation also, if 2(3.14)<=x<=2(3.14) Answered by Harley Weston. 





John Napier and e 
19990206 

From Shimin: I would like to ask about the exact definition of e, its history (like how John Napier came about discovering it) and its applications in problems and real life situations. Thank you! Answered by Chris Fisher. 





Logs 
19981021 

From Benny: What does log means? How come we have to use log Answered by Chris Fisher. 





Two Problems 
19980728 

From James Pulver: How do you solve these problem? If log abc=16 and log ac=12 , find b. (The logs are log base 10.) and If a and b are real numbers, i^2 = 1 and (a+b)+5i=9+ai what is the value of b? Answered by Jack LeSage. 





A Problem with Logs. 
19971126 

From Herman: Given log 24=a, log 25=b and log 26=c, express log 39 in terms of a, b and c. Answered by Penny Nom. 





Natural Logarithm Functions 
19970423 

From Rickson: The following two questions are some of my son's homework that he is having trouble with......any advice or assistance would be appreciated. (eX)5=1000.............the X and 5 are exponents lnx + ln(x+3) = ln10 In each question the problem is to find x. Answered by Harley Weston. 

