SOLUTION: State the value of x that satisfies 4^(2x-3)=2

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Question 1095187: State the value of x that satisfies 4^(2x-3)=2
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52931) About Me  (Show Source):
You can put this solution on YOUR website!
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4%5E%282x-3%29 = 2 ====>  2%5E%282%2A%282x-3%29%29 = 2  ====>  2%5E%284x-6%29 = 2 ====>  4x-6 = 1  ====>  4x = 1 + 6 = 7  ====>  x = 7%2F4.


Answer by MathTherapy(10559) About Me  (Show Source):
You can put this solution on YOUR website!

State the value of x that satisfies 4^(2x-3)=2
4%5E%282x+-+3%29+=+2

%282%5E2%29%5E%282x+-+3%29+=+2 ------ Converting 4 to base 2

2%5E%282%282x+-+3%29%29+=+2%5E1

2(2x - 3) = 1 ------ Bases are equivalent and so are the exponents

4x - 6 = 1

4x = 7

highlight_green%28matrix%281%2C3%2C+x%2C+%22=%22%2C+7%2F4%29%29