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.
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
$