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

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Answer 1 · 2015-12-17T04:07:21

#f^-1(x)=log_5x#

Write as #y=5^x#.

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

#x=5^y#

#log_5x=Log_5(5^y)#

#log_5x=ylog_5 5#

#log_5x=y#

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

#f^-1(x)=log_5x#