Question

e^(x-2)-12^(2x+3)=0

Class is a college level math prep.
Sorry for previous post being incomplete.


I'm thinking:

ln^(x-2)=ln12^(2x+3)

(x-2)ln=(2x+3)ln12

xln-2ln=2xln(12)+3ln(12)

xln-2xln(12)= 2ln+3ln(12)

and not sure

Answer 1

Your notation is incorrect.
"2ln" doesn't mean anything

By definition, ln(e^k) = k
so, let's start over:

e^(x-2) = 12^(2x+3)

take ln of both sides:

x-2 = (2x+3) ln 12
x - 2 = 2ln12 x + 3ln12
x(1 - 2ln12) = 2 + 3ln12

x = (2 + 3ln12)/(1 - 2ln12)