SOLUTION: solve for x 2 to the power of x + 5 = 3 to the power of x I know the answer is x=2....but I cant prove it.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: solve for x 2 to the power of x + 5 = 3 to the power of x I know the answer is x=2....but I cant prove it.      Log On


   

Question 254778: solve for x
2 to the power of x + 5 = 3 to the power of x
I know the answer is x=2....but I cant prove it.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The answer can't be 2.
2%5E%282%2B5%29=128
3%5E%282%29=9
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Take the log (base 2) of both sides.
Convert the right hand side to base 2.
log%282%2C3%5E%28x%29%29=log%283%2C3%5E%28x%29%29%2Flog%283%2C2%29
The equation then becomes,
x%2B5=x%2F%28log%283%2C2%29%29
x%2A%281-1%2Flog%283%2C2%29%29=5
x=5%2F%281-1%2Flog%283%2C2%29%29
Approximately, the answer is
x=8.55
2%5E%288.55%2B5%29=11993
3%5E%288.55%29=12005