TITLE: Simplifying log
QUESTION [5 upvotes]: I have been told that $10^{\log_{10}(x)}$ is simply x
I have also been told that $10^{\log_{10}}$ are the inverse of each other and cancel each other out but am having trouble understanding this.
Can somebody kindly explain how the above is simply x and how the $10^{\log_{10}}$ are inverses?
Thank you.

REPLY [4 votes]: Note that by definition
$$y=\log_{10} x\iff  10^y=x\iff 10^{\log_{10}x}=x$$ 
and more in general
$$c=\log_{a} b\iff  a^c=b\iff a^{\log_{a}b}=b$$
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