Question

find the inverse of $y = \ln(x - 5) + 3$.

the inverse function is $y = \square$.

Explanation:

Step1: Swap x and y variables

$x = \ln(y - 5) + 3$

Step2: Isolate the natural log term

$x - 3 = \ln(y - 5)$

Step3: Convert to exponential form

$e^{x - 3} = y - 5$

Step4: Solve for y

$y = e^{x - 3} + 5$

Answer:

$y = e^{x - 3} + 5$