inverse of ln(x+9) — step-by-step solution

The function domain is

x > -9

The logarithm of a nonconstant affine function is strictly monotone on its domain and takes every real value

Express input

x

in terms of output

y

y = \ln (x + 9)

⇥Let's solve in

ℝ

\ln (x + 9) = y

⇥Let's apply the exp function on both sides:

⇥

e^{\ln (x + 9)} = e^{y}

⇥

x + 9 = e^{y}

⇥Solution found:

x = e^{y} - 9

Renaming the output as

x

, the inverse is

e^{x} - 9

, with domain

x \in ℝ

▶Inverse function:

e^{x} - 9