exponent powers

Question

0

450

1

+12

If $x$ is a real number such that $2^{2x+3}=14$ , find $2^x$ . Thank you!

LoryLullic Jul 31, 2020

Guest · Answer 1 · 2020-07-31T03:40:24

Solve for x over the real numbers:
2^(2 x + 3) = 14

Take the logarithm base 2 of both sides:
2 x + 3 = log(14)/log(2)

Subtract 3 from both sides:
2 x = log(14)/log(2) - 3

Divide both sides by 2:

x = log(14)/(2 log(2)) - 3/2 ≈0.403677