Answer:
[tex]x=\frac{10^{x}-3}{2}[/tex]
Step-by-step explanation:
A logarithm is the inverse of an exponent, that is:
[tex]y=log_{b}(x)\\b^{y}=x[/tex]
Using this property we can solve x and get the inverse function:
[tex]f(x)=log(2x+3)\\\\y=log(2x+3)\\\\10^{y}=2x+3\\\\x=\frac{10^{y}-3}{2}\\\\y=\frac{10^{x}-3}{2}\\\\\\g(x)=f^{-1}(x)=\frac{10^{x}-3}{2}[/tex]
