1)
↪y=ln(x-1)
Interchange role of x and y,
↪x=ln (y-1)
Changing it to exponential form,
↪e^x=y-1
↪y=e^x+1
↪inverse of f(x)=y=e^x +1
2)
↪y=ln(2x)
Interchange role of x and y,
↪x=ln(2y)
Changing it to exponential form,
↪e^x=2y
↪y=(e^x)/2=inverse of f(x)
3)
↪y=e^3x
Interchange role of x and y,
↪x=e^3y
Take log on both sides,
↪ln x= ln {(e)^3y}
I have used property of log here to further simplify...
↪ln x= 3y × ln(e)
↪ln x=3y × 1 {as ln e=1}
↪y=ln(x)/3 =inverse of f(x)
