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How do I find the inverse function of $y=f(x)=10^x$? As per my knowledge I have to swap $x$ for $y$. In that case it'll be $x=10^y$. Is that correct?

Dando18
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gmail user
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1 Answers1

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$$ f(x)=y=10^x $$

you are correct in finding the inverse of a function by swapping the variables, so

$$ \begin{align*} &f^{-1}(x) = x = 10^y \\ &f^{-1}(x) = y = \log_{10}(x) \quad (1) \end{align*}$$

where $ f^{-1}(x) $ is the inverse of $f(x)$

$(1)$ This step uses the property of logarithms that $x=b^y \implies y=\log_b(a)$

Dando18
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  • I didn't get the 3rd step. Why did you add Log x? Why you again swap x and y? – gmail user Mar 14 '17 at 01:42
  • One last thing, may be silly. As author again swap x and y after in example of http://www.purplemath.com/modules/invrsfcn3.htm. Do I need to swap them again after step 2? That's where my main confusion is. – gmail user Mar 14 '17 at 02:19
  • @gmailuser You only need to swap once and then solve for $y$. This is, however, not the same equation as you started with, it is the inverse. – Dando18 Mar 14 '17 at 15:21