[tex]ALGEBRA \\ \\ \\
f(x) \: = \: \: {3}^{x } \\ \\ Let \: \: y \: = \: {3}^{x} \\ \\ To \: find \: inverse \: , \: first \: interchange \: the \: \\ variables \: - \\ \\ We \: get \: , \\ x \: = \: {3}^{y } \\ \\ Taking \: log \: both \: sides \: - \\ \\ log(x ) \: = \: log( {3}^{y} ) \\ \\ log(x) \: = \: y \: log(3) \\ \\ y \: = \: \frac{ log(x) }{ log(3) } \\ \\ Using \: property \: of \: logarithms \: \\ \\ y = log_{3}(x) \\ \\ Hence \: , \: inverse \: of \: the \: given \: function \: \\ is \: - \: \\ \\ \\ \: {f}^{ - 1}( x) \: = \: log_{3}(x) \: \: \: \: \: \: Ans.[/tex]
