SOLUTION: Solve the equation. 15^x=5^(x+2)

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Question 371060: Solve the equation. 15^x=5^(x+2)
Found 2 solutions by robertb, Edwin McCravy:
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
take logs of both sides:
x*log15 = (x+2)*log5,
xlog15 = xlog5 + 2log5,
xlog15- xlog5 = 2log5,
x(log15-log5) = 2log5,
xlog(15/5) = 2log5,
xlog3 = 2log5,
x = 2log5/log3.

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
15%5Ex=5%5E%28x%2B2%29
Take logs of both sides

log%2815%5Ex%29=log%285%5E%28x%2B2%29%29

x%2Alog%2815%29=%28x%2B2%29log%285%29

x%2Alog%2815%29=x%2Alog%285%29%2B2%2Alog%285%29

Get both terms that contain x alone on the left.

x%2Alog%2815%29-x%2Alog%285%29=2%2Alog%285%29

Factor out x

x%28log%2815%29-log%285%29%29=2%2Alog%285%29

Divide both sides by that big parentheses:

x=%282%2Alog%285%29%29%2F%28log%2815%29-log%285%29%29+

You can get the numerical approximation from that 
or you can simplify some more.

x=%282%2Alog%285%29%29%2Flog%2815%2F5%29+

x=%282%2Alog%285%29%29%2Flog%283%29+

x=2.929947041

Edwin