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.

Thx in advance.

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- Oct 1st 2009, 06:18 AMSolid8Snakequestion 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.

Thx in advance. - Oct 1st 2009, 06:28 AMmathaddict
HI

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

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

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

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

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

Now back to your question :

$\displaystyle

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

$