Simplifying log

Question

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.

Answer 1

Note that by definition

$$y=\log_{10} x\iff 10^y=x\iff 10^{\log_{10}x}=x$$

and more in general

$$c=\log_{a} b\iff a^c=b\iff a^{\log_{a}b}=b$$