Answer
a.) $e^2 = (x+1)$
b.) $ e^4 = (x-1)$
Work Step by Step
$Express$ $the$ $equation$ $in$ $exponential$ $form:$
a.) $\ln (x+1) = 2$
b.) $\ln (x-1) = 4$
Natural Log form to exponential form: $\ln a = b \rightarrow e^b = a$ [Note: e means euler's number, NOT a variable]
a.) $\ln (x+1) = 2$
Plug in (x+1) for a and 2 for b
$\ln (x+1) = 2 \rightarrow e^2 = (x+1)$
b.) $\ln (x-1) = 4$
Plug in (x-1) for a and 4 for b
$\ln (x-1) = 4 \rightarrow e^4 = (x-1)$