SOLUTION: 3^(2x-1) = 10*(3^x)-3. "How to solve x?" thank you

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Question 313118: 3^(2x-1) = 10*(3^x)-3. "How to solve x?" thank you
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
3%5E%282x-1%29+=+10%2A%283%5Ex%29-3
3%5E%282x%29%2F3=10%2A3%5E%28x%29-3
Substitute u=3%5Ex, then u%5E2=3%5E%282x%29
u%5E2%2F3=10%2Au-3
u%5E2=30u-9
u%5E2-30u%2B9=0
Use the quadratic formula,
u+=+%28-%28-30%29+%2B-+sqrt%28+%28-30%29%5E2-4%2A1%2A9+%29%29%2F%282%2A1%29+
u+=+%2830+%2B-+sqrt%28+900-36+%29%29%2F%282%29+
u+=+%2830+%2B-+sqrt%28+864%29%29%2F%282%29+
u+=+%2830+%2B-+12sqrt%28+6%29%29%2F%282%29+
u+=+15+%2B-+6sqrt%28+6%29+
Two solutions:
u1=15%2B6sqrt%286%29
3%5E%28x%29=15%2B6sqrt%286%29
x=log%283%2C%2815%2B6sqrt%286%29%29%29
x=log%2810%2C%2815%2B6sqrt%286%29%29%29%2Flog%2810%2C%283%29%29+
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u2=15-6sqrt%286%29
3%5E%28x%29=15-6sqrt%286%29
x=log%283%2C%2815-6sqrt%286%29%29%29
x=log%2810%2C%2815-6sqrt%286%29%29%29%2Flog%2810%2C%283%29%29+