# Find the inverse of the function f(x)=ln(5x+1)-6?

Feb 6, 2017

Inverse of $\ln \left(5 x + 1\right) - 6 \text{ }$ is $\text{ } \frac{{e}^{\left(x + 6\right)} - 1}{5}$

#### Explanation:

Let $y = f \left(x\right) = \ln \left(5 x + 1\right) - 6$

Hence, $\ln \left(5 x + 1\right) = y + 6$

or $5 x + 1 = {e}^{\left(y + 6\right)}$

or $x = \frac{{e}^{\left(y + 6\right)} - 1}{5}$

Hence, inverse of $\ln \left(5 x + 1\right) - 6$

is $\frac{{e}^{\left(x + 6\right)} - 1}{5}$