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.

They are inverse eash other by definition! How do you define $\log_{10}$? — Crostul, Feb 13 '18 at 20:56
put the dollar sign symbol before and after each math expression: 10^{\log_{10}(x)} $\rightarrow 10^{\log_{10}(x)}$ — Alex Jones, Feb 13 '18 at 20:56

score 4 · Accepted Answer · answered Feb 13 '18 at 20:55

4

Note that by definition

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

and more in general

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

answered Feb 13 '18 at 20:55

user

1

Thank you for the answer. Yes it makes sense now. Thank you to all those that edited and commented. – Y.M.80 Feb 13 '18 at 22:36
Well done! You are welcome, Bye! – user Feb 13 '18 at 22:37

1 Answers1