Given the function #f(x) = log_3(x+4)#, what is the value of #f^-1(3)#?

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Answer 1 · 2016-04-28T20:54:18

#f^-1(3)=23#

Given,

#f(x)=log_3(x+4)#

We must first determine the inverse of the logarithm. To do this, rewrite the logarithm in exponential form.

#y=log_3(x+4)#

#3^y=x+4#

Swap the positions of #x# and #y#.

#3^x=y+4#

Solve for #y#.

#y=3^x-4#

Substitute #x=3#.

#y=3^3-4#

Solve for #y#.

#y=27-4#

#y=23#

#color(green)(|bar(ul(color(white)(a/a)color(black)(f^-1(x)=23)color(white)(a/a)|)))#