SOLUTION: I need to solve an equation where the exponent is the variable, and obviously I can't figure it out properly. I can get the correct answer by guessing but not with proper technique

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Question 107586This question is from textbook College Preparatory Math Algebra 2
: I need to solve an equation where the exponent is the variable, and obviously I can't figure it out properly. I can get the correct answer by guessing but not with proper techniques. Can anyone help show me the correct method? The problem is solve for x given 8^x=4. Thank you. This question is from textbook College Preparatory Math Algebra 2

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
8%5Ex+=+4
The key is to express 8 and 4 as powers of 2
8+=+2%5E3
4+=+2%5E2
8%5Ex+=+%282%5E3%29%5Ex
%282%5E3%29%5Ex+=+2%5E%283x%29
2%5E%283x%29+=+2%5E2
The bases are the same, so the exponents must be equal
3x+=+2
x+=+2%2F3 answer
This is easy to verify with a calculator