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A problem with logarithms 2019-08-23
From Iriogbe:
Find the value : if log3 (a-6) =2b and log2 (a-7) =3b
Answered by Penny Nom.
4^x=2^x+6 2019-04-05
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 2019-02-28
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 2019-01-28
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 2017-12-10
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 2017-11-28
From Chhavi:
Find f'(x).

Answered by Penny Nom.
3^2x-5=27 2016-12-14
From danaja:
solve for the following 3^2x-5=27
Answered by Penny Nom.
Find two values of x satisfying f(x)=1 where f(x)=sin(ln(x)) 2016-01-21
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 2015-05-18
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 2014-10-26
From Susan:
Solve for x: logbase4 (sin x) = -0.5
Answered by Penny Nom.
Logarithms 2014-08-28
From effaryna:
how logarithms is applied in everyday life?
Answered by Penny Nom.
Differentiate ln[x(2x-4)^1/2] 2014-06-28
From Igwe:
If y=In[x(2x-4)^1/2],find dy/dx at x=3
Answered by Penny Nom.
How do we use logarithms in our daily life 2014-06-01
From ss:
how do we use logarithms in our dailylife
Answered by Penny Nom.
Evaluate log3 14 2013-11-17
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 2013-06-15
From Samantha:
I can't seem to understand how to solve for x when it is in power form, here is the equation:


Answered by Penny Nom.
How do i write log_8(P) =7 in exponential form? 2013-04-14
From nancy:
How do i write this in exponential form log8P =7
Answered by Penny Nom.
Solve 8 logx > x 2013-02-19
From Fulvio:
Hi, could you solve this equation in algebraic form:


Answered by Harley Weston.
What is the domain of f(x)=sin(ln(x))/ln(x)? 2013-02-06
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 2012-04-25
From Kristina:
what is the exponential form of log8=P
Answered by Penny Nom.
A log equation in exponential form 2011-11-11
From Sarah:
Express the equation in Exponential form

log2 to the 16th power=4

Answered by Penny Nom.
Uses of logarithms 2011-11-09
From BEA:
what is the use of logarithmic functions in real life or daily life?
Answered by Penny Nom.
Exponential form 2011-05-18
From Kara:
How do I write this in exponential form?

log 1/8 = -3

Answered by Penny Nom.
ln(12 x) = 6 2011-03-03
From Carolyn:
solve the equation

ln12x = 6

Thank you


Answered by Penny Nom.
Daily life example of logarithms 2011-02-04
From owais:
what are the application or daily life example of logarithms?
Answered by Harley Weston.
Simplify the logarithmic expression 2010-12-02
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 2010-09-27
From mindy:
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) 2010-04-28
From Alex:
y= - log(x), where y = 4.3
solve for x.

Answered by Harley Weston.
Log[f(x)] 2010-03-08
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 2009-08-05
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 2009-07-08
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 2009-05-19
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 2009-03-07
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 2009-03-06
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? 2009-03-02
From Charlene:
If 5 to the power of y = 625, what is y?
Answered by Penny Nom.
A log base 2 problem 2008-11-26
From dave:
solve for x

(log base 2 of x) - (log base 2 of (x-2)) = 3

Answered by Penny Nom.
How do you solve "logx^4=4? 2008-11-17
From Scott:
How do you solve "logx^4=4"?
Answered by Penny Nom.
2^x = 1,000,000 2008-09-06
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 2008-08-25
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 2008-06-27
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 (logx-log(x-1)) 2008-05-22
From kritica:
lt x->0 (logx-log(x-1))
Answered by Harley Weston.
Which is larger, 727464^512693 or 624610^518548? 2008-05-18
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 2008-05-03
From keith:
please help me find the inverse of this function:

h(t) = 2 + 4 ln(1-5t)

Answered by Stephen La Rocque.
log2x+log(x+4)=1 2008-04-12
From ryan:
solve the equation for x, log2x+log(x+4)=1
Answered by Penny Nom.
1-(1-P)^75=0.05 2008-04-05
From Amy:
Answered by Stephen La Rocque and Penny Nom.
ln (x) - x = ln (2) 2007-11-18
From James:
How do you make x the subject of

ln (x) - x = ln (2)

Answered by Stephen La Rocque.
Logs and exponentials 2007-07-31
From Marsia:
Explain how the functions of exponents and logarithms relate to each other.
Answered by Penny Nom.
loga b + logb a < 0 2007-07-08
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 loga b + logb a < 0
Answered by Penny Nom.
log(0.81) 2007-06-28
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 2007-06-27
From alex:
y = log base 2 of lag base 2 of x The slope of the tangent to the given curve at its x-intercept is..?
Answered by Harley Weston.
Understanding log equations 2007-05-10
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? 2007-04-11
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 2007-02-27
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 2006-11-26
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? 2006-06-14
From Trang:
How many digits are in the number 264?
Answered by Stephen La Rocque.
An equation involving logarithms 2006-03-05
From Chris:
Given that loge y = 0.3logex+1.2 show that y=3.32 x0.3

Answered by Penny Nom.
6^(x+1) = 12^(x-3) 2006-02-05
From BB:
6x+1 =12x-3
Answered by Penny Nom.
Differentiation, powers and logs 2006-01-06
From Claudia:

Question: how do I find the derivative of

x* ln(x+(e^2))^2



Answered by Penny Nom.
cos x * cos 2x * cos 4x * cos 8x 2005-08-29
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. 2005-08-26
From Alain:

I have the following equation:

y = ln(x) + x

How do I solve for x?

Answered by Penny Nom.
Extraneous solutions 2005-02-04
From Heather:
My teacher wants to know why there are extraneous solutions in logarithms?
Answered by Penny Nom.
Some logarithm problems 2005-01-27
From Jo:
Given ln x=7.1; ln y=8.2, Find ln(x^3y^7)
Answered by Penny Nom.
ln(hx+n) 2005-01-07
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 2004-08-02
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 2004-07-14
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 2004-06-21
From Un eleve:
(ln(50/x)) / (ln(40/x)) = a = constante

comment extraire la variable x ???

Answered by Claude Tardif.
Logs 2004-02-29
From Sandy:
find X

my book uses prop 7 to rewrite as logb4raised3/2-logb8raised2/3+logb2=logbx; then writes logb8-logb4+logb2=logbx how did it get here?

Answered by Claude Tardif.
A problem with logs 2004-02-22
From Caitlyn:
problem: ln x + ln (x-2) = 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 2004-02-01
From A student:
Where did the word logarithmic come from? Where/whom did it originate?
Answered by Harley Weston.
Domain of a function 2003-10-14
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 2003-09-16
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 2003-07-22
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 2001-07-29
From Rajesh:
what is greater 19991997 or 19971999?
Answered by Chris Fisher.
Two log problems 2001-06-16
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
  1. (log base 7 * 10) * (log base 10 * X ) = 2

  2. log base 10 * (3x-4) + log base 12 * X
    (log base 12 * 2) + (log base 12 * 5)

    = log base 10 *4

Answered by Harley Weston.
An integration problem 2000-11-30
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? 2000-10-11
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 2000-09-12
From Becky:
How do they get these answers?
  1. log 8 + log 2 = ?
    Answer is: log 16

  2. 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 2000-05-18
From Catherine Sullivan:
Please help me with the following: The radioactive isotope carbon-14 is present in small quantities in all life forms, and it is constantly replenished until the organism dies, after which it decays to carbon-12 at a rate proportional to the amount of C-14 present, with a half life of 5730 years. Suppose C(t) is the amount of C-14 at time t.
  1. Find the value of the constant k in the differential equation: C'=-kC
  2. 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 C-14 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 2000-05-01
From Kaushal Shah:
How Do WE Integrate the following Functions,
  1. Integral xtanx dx
  2. How was natural base "e" discovered and why e=2.7.......

Answered by Claude Tardif.
Logs 2000-04-12
From Jessica:
Write as a single log 3ln x - 2ln(y+e) + 5ln(x-12) - 4ln y
Answered by Harley Weston.
Characteristic of a logarithm 2000-03-14
From Andrew Strauss:
What is the characteristic of log base 18 of 1980 ?
Answered by Harley Weston.
Logarithms 2000-01-18
From Jennifer:

Hi I have a test tomorrow and I was wondering if you could help me with these two problems.

  1. Explain how to express y in terms of x if log3y=4log3(2X)

  2. 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 1999-12-16
From Pierre:
Can you please answer those three question

  1. 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.

  2. .

Answered by Harley Weston.
Log Cancel 1999-12-03
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 1999-11-16
From Gina Renicker:
The derivative of:

y=e(xlnx) and y=x2arctan(x1/2)
Answered by Harley Weston.

Derivatives with logs 1999-10-26
From Kate:
What is the derivative of 5 to the 5x-2 at x equals 0.8?
Answered by Harley Weston.
-log(a) 1999-10-22
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 1999-10-11
From Rich Bolton:
Here's my question:


Can you please show me how to do this?
Answered by Penny Nom.

A log problem 1999-05-08
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 1999-02-06
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 1998-10-21
From Benny:
What does log means? How come we have to use log
Answered by Chris Fisher.
Two Problems 1998-07-28
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.)
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. 1997-11-26
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 1997-04-23
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.




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