Date: Sun, 23 Nov 1997 04:15:38 -0600 (CST)
Subject: Log

Name: Herman

Who is asking: Student
Level: Secondary

Given log 24=a, log 25=b and log 26=c, express log 39 in terms of a, b and c.

Hi Herman,

I like this problem. What you need to do is make liberal use of the facts that log(p*q)=log(p) + log(q) and log(p^q)=q*log(p).

Thus log(39)=log(3) + log(13),

c=log(26)=log(2) + log(13),

b=log(25)=2*log(5) and

a=log(24)=3*log(2) + log(3).

Hence a+c=3*log(2) + log(3) + log(2) + log(13) = log(39) + 4*log(2) and thus

log(39) = a + c - 4*log(2).

To deal with the log(2) recall that log(10)=1 so

1=log(10) = log(2) + log(5) = log(2) + b/2, or

log(2) = 1-b/2.

Thus log(39) = a + c - 4*log(2) = a + c -4(1-b/2).


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