Question

solve \ln(x + 5) + 3 = 2

select one:
a. \\( x = e^{-1} \\)

b. \\( x = e^{-1} - 5 \\)

c. \\( x = -6 \\)

d. \\( x = e^{5} + 5 \\)

Explanation:

Step1: Isolate the logarithmic term

Subtract 3 from both sides.
$\ln(x+5) + 3 - 3 = 2 - 3$
$\ln(x+5) = -1$

Step2: Convert to exponential form

Use $e^{\ln(a)}=a$ for the left side.
$e^{\ln(x+5)} = e^{-1}$
$x+5 = e^{-1}$

Step3: Solve for x

Subtract 5 from both sides.
$x = e^{-1} - 5$

Answer:

B. $x = e^{-1} - 5$