Question

Pre-calc,
I am so stuck. Please help:
Solve:
12^(2x-1) = e^(x+1)

Answer 1

divide both sides by e^(x + 1)

12^(2x - 1)e^(-1 -x) = 1 (note the sign changes because i moved e^(x + 1) from the denominator to the numerator)

write the exponents in 12^(2x - 1)e^(-1 -x) = 1 in terms of a common base

12^(2x - 1)e^(-1 -x) = e^log(12^2x - 1)e^log(e^-1 -x) = e^( (2x - 1)log(12) ) e^( (-1 -x) log(e) ) = e^(-1 -x + (2x - 1) log(12) )

eliminate the exponential from the left hand side:
-1 -x + log(12)(2x-1) = 0

clean things up:

(2log(12) -1)x = 1 + log(12)

x = 1 / (2(log(12) -1) + log(12) / (2log(12) - 1)

be mindful of the parentheses in all steps, they are important.

Answer 2

processing...