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

Answer 1

To find the inverse of ( f(x) = 5^x ), you switch the roles of ( x ) and ( y ) and solve for ( y ). Then, ( y ) becomes the inverse function of ( f(x) ).

[ y = 5^x ]

Swap ( x ) and ( y ):

[ x = 5^y ]

Now, solve for ( y ):

[ \log_5(x) = y ]

Thus, the inverse function of ( f(x) = 5^x ) is ( f^{-1}(x) = \log_5(x) ).

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Answer 2

Ariana Alvarez

#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#

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Answer from HIX Tutor

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