$y={2.1}^{x}$
Interchange $x$ and $y$$x={2.1}^{y}$
Swap the sides of the equation${2.1}^{y}=x$
Convert the decimal into a fraction${\left( \frac{ 21 }{ 10 } \right)}^{y}=x$
Take the logarithm of both sides of the equation$y=\log_{ \frac{ 21 }{ 10 } }({ x })$
Substitute $f^{-1}\left( x \right)$ for $y$$f^{-1}\left( x \right)=\log_{ \frac{ 21 }{ 10 } }({ x })$