Question

How to simplify 2^(2x+3) = 2^(x+1) + 3

Answer 1

2^(2x+3) = 2^(x+1)+3
ln[2^(2x+3)] = ln[2^(x+1)]+ln[3]
(2x+3)ln[2] = (x+1)ln[2]+ln[3]
(2x+3)ln[2] - (x+1)ln[2] = ln[3]
(2x+3-x-1)ln[2] = ln[3]
(x+2)ln[2] = ln[3]
2^(x+2) = 3

Answer 2

...or if you need to solve for x,

From (x+2)ln[2] = ln[3]
(x+2) = ln[3]/ln[2]
x = (ln[3]/ln[2]) - 2