# question regarding logs

• Oct 1st 2009, 06:18 AM
Solid8Snake
question regarding logs
hello! there is a question 10to the power of 2log 4 and it is asking me to simplify, but im not too sure how to go about. the base for the log is 10 and not 4 if you were wondering.

• Oct 1st 2009, 06:28 AM
Quote:

Originally Posted by Solid8Snake
hello! there is a question 10to the power of 2log 4 and it is asking me to simplify, but im not too sure how to go about. the base for the log is 10 and not 4 if you were wondering.

HI

$x^{\log_x(y)}=y$

Proof : Let $x^{\log_x(y)}=p$ and lets see if $p=y$

Knowing that $a^x=y\Rightarrow \log_a{y}=x$

$\log_x{p}=\log_x{y}$

cancelling the logs , we get p=y so the above is correct .

Now back to your question :

$
10^{2\log_{10}{4}}=10^{2\log_{10}{4^2}}=16
$