SOLUTION: Solve the equation 7^(x – 2) = 5^x. Round the answer to four decimal places.

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Question 623003: Solve the equation 7^(x – 2) = 5^x. Round the answer to four decimal places.
Found 2 solutions by MathTherapy, lwsshak3:
Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the equation 7^(x – 2) = 5^x. Round the answer to four decimal places.

7%5E%28x+-+2%29+=+5%5Ex

(x - 2) log 7 = x log 5

%28%28x+-+2%29+log+7%29%2Fx+=+%28x+log+5%29%2Fx

%28%28x+-+2%29+log+7%29%2Fx+=+cross%28x%29+log+5%2Fcross%28x%29

%28%28x+-+2%29+log+7%29%2Fx+=+log+5

%28%28%28x+-+2%29+log+7%29%2Fx%29%2Flog+7+=+log+5%2Flog+7

%28%28%28x+-+2%29+cross%28log+7%29%29%2Fx%29%2Fcross%28log+7%29+=+log+5%2Flog+7

%28x+-+2%29%2Fx+=+log+5%2Flog+7

%28x+-+2%29%2Fx+=+0.827087475

x - 2 = 0.827087475x ----- Cross-multiplying

x - 0.827087475x = 2

.172912525x = 2

x+=+2%2F.172912525, or 11.56654212 ≈ highlight_green%2811.5665%29

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Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the equation 7^(x – 2) = 5^x. Round the answer to four decimal places.
**
7^(x – 2) = 5^x
take log of both sides
(x-2)log7=xlog5
(x-2)/x=log5/log7≈.8271
x-.8271x=2
.1729x=2
x≈2/.1729
x≈=11.5665