# Logarithm simplification help

• Nov 21st 2010, 01:48 AM
BinaryBoy
Logarithm simplification help
Hi all,

I've just been working with logarithms and I've stumbled across a problem with one equation:

$log3(4)^2 + 3 log3(2)$

According to the book, the answer is log3(2), however I am not getting that when I equate the powers and receive log3(16) + log3(8), which equals log3(128).

Any help solving this problem will be greatly appreciated!

Thanks,

Nathaniel
• Nov 21st 2010, 02:34 AM
pickslides
Maybe it was meant to be

$\log_3(4)^2 - 3 \log_3(2) = \log_3(16) - \log_3(8) =\log_3(16\div 8) = \log_3(2)$
• Nov 21st 2010, 01:10 PM
BinaryBoy
Thanks for the reply, picksides. Actually, funny thing, when I was writing the original question above, I accidentally put a negative sign instead. Well, when I evaluated I saw the answer was the same and for a moment I was joyful...

But I think you're quite right. :)

Thanks!