Question 1134309
{{{f(x) = log(3 ,(x + 1))}}}, 

what is {{{f^-1(2)}}}

first find inverse {{{f^-1(x)}}}

replace {{{f(x)}}} with {{{y}}}

{{{y= log(3 ,(x + 1))}}}...swap {{{x}}} and {{{y}}}

{{{x= log(3 ,(y + 1))}}}....solve for {{{y}}}; 

apply rule for logarithmic equations, {{{log(b,a)=c}}}  is equivalent to{{{ b^c=a}}}
 
in your case {{{b=3}}},{{{a=y+1}}} and {{{c=x}}}

{{{ 3^x=y+1}}}

{{{ y=3^x-1}}}

{{{f^-1(x)=3^x-1}}}

=>
{{{f^-1(2)=3^2-1}}}

{{{f^-1(2)=8}}}


{{{drawing( 600, 600, -10, 10, -10, 10,
circle(2,8,.12),locate(2,8,p(2,8)),
 graph( 600, 600, -10, 10, -10, 10, log(3,(x + 1)), 3^x-1)) }}}