How do you find the inverse of $f (x) = 5^{x}$ $f(x) = 5^x$ ?

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Answer 1 · 2015-12-17T04:07:21

$f^{- 1} (x) = {log}_{5} x$ $f^-1(x)=log_5x$

Write as $y = 5^{x}$ $y=5^x$ .

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

$x = 5^{y}$ $x=5^y$

${log}_{5} x = {log}_{5} (5^{y})$ $log_5x=Log_5(5^y)$

${log}_{5} x = y {log}_{5} 5$ $log_5x=ylog_5 5$

${log}_{5} x = y$ $log_5x=y$

Rewrite with $f^{- 1} (x)$ $f^-1(x)$ , which denotes an inverse function.

$f^{- 1} (x) = {log}_{5} x$ $f^-1(x)=log_5x$

How do you find the inverse of f(x)=5xf(x) = 5^x?