How do you solve a equation by converting to logarithm form for the problem$3e^{x-4} +2=83$?

Question

$3e^{x-4} +2=83$ I understand converting logarithms but i dont understand how to convert e into log form and solve. help would be deeply appreciated.

Answer 1

$3e^{x-4} +2=83$, subract two from both sides:

$3e^{x-4}=81$, and after dividing by $3$ and taking the natural log of both sides, we have:

$(x-4)=\ln(27)$, and so:

x = $ln(27)+4$

Answer 2

Notice

$$ 3 e^{x-4} + 2 = 83 \iff 3 e^{x-4} = 81 \iff e^{x-4} = 27 \iff x - 4 = \ln 27 \iff \boxed{x = \ln 27 + 4 } $$

Answer 3

$$ 3e^{x-4}+2 = 83 \leftrightarrow 3e^{x-4} =81 \leftrightarrow e^{x-4} = 27 \leftrightarrow \ln\left(e^{x-4}\right)= \ln(27)\leftrightarrow x-4 = \ln(27) \leftrightarrow x= \ln(27)+4 $$