How do you find the inverse of $f (x) = {log 7}^{x}$ $f(x) = log7^x$ ?

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Answer 1 · 2015-12-31T00:59:10

$f^{- 1} (x) = \frac{x}{log 7}$ $f^-1(x)=x/log7$

Write as $y = log (7^{x})$ $y=log(7^x)$ .

Switch the $x$ $x$ and $y$ $y$ , then solve for $y$ $y$ .

$x = log (7^{y})$ $x=log(7^y)$

Rewrite using logarithm rules.

$x = y log 7$ $x=ylog7$

$y = \frac{x}{log 7}$ $y=x/log7$

This can be written in function notation:

$f^{- 1} (x) = \frac{x}{log 7}$ $f^-1(x)=x/log7$

These graphs should be reflections over the line $x = y$ $x=y$ .

graph{(y-log(7^x))(y-x/log7)=0 [-18.02, 18.02, -9.01, 9.01]}

How do you find the inverse of f(x) = log7^xf(x)=log7xf(x) = log7^x?