Is there a way to change the base of a logarithm without the change of base formula and without a calculator? I believe it has to do with base 10 representation?

Question

anonymous · Answer

tell u the truth... i never use the cob formula...

anonymous · Answer

lol ok...it's crucial for me though when I'm not allowed to use a calculator...

anonymous · Answer

give an example of what u wanna change...

anonymous · Answer

Anything really...if there are any restrictions, then something within them?

anonymous · Answer

ok, how bout this... change $\log_2 32=x $ to log base 10...
first i change to exponential form:  $\large 2^x = 32 $
then take log base 10 of both sides... $\large log2^x = log32\rightarrow xlog_2=log32 $
then isolate x.... is that what u mean?

anonymous · Answer

That doesn't look familiar...I saw someone do it before, but I don't recall...what I saw had powers of 10 in the denominators and things like that.

anonymous · Answer

oops that should be $\large xlog2  $ not $\large xlog_2  $

anonymous · Answer

so you're actually looking for the value for logs without the aid of a calculator... is that what u mean?

anonymous · Answer

Um...I don't think so...like they literally changed the logarithm using something called base ten representation. It turned something like $\log_3x \implies \log_5 something$

anonymous · Answer

$\large log_3 x = y\rightarrow 3^y=x $
take the log base 5 of both sides:
$\large log_5 (3^y)=log_5 x\rightarrow ylog_5 3=log_5 x\rightarrow y=\frac{log_5 x}{log_5 3} $
like that?

anonymous · Answer

I think that will work :) I'll ask my friend who did it when I get the chance. Thanks for the help though :D

anonymous · Answer

ok... i'm curious what u find out... pls post a "post" post of this when u get the answer u needed... 
yw...:)

anonymous · Answer

alright I will try to remember to do that :) (I don't see my friend until school stats again)