SOLUTION: solve the equation 2^5x=8^x+6 please help me solve this equation

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Question 197260: solve the equation
2^5x=8^x+6
please help me solve this equation
Answer by jim_thompson5910(28717) About Me  (Show Source):
You can put this solution on YOUR website!
2%5E%285x%29=8%5E%28x%2B6%29 Start with the given equation.


2%5E%285x%29=%282%5E3%29%5E%28x%2B6%29 Rewrite 8 as 2%5E3


2%5E%285x%29=2%5E%283%28x%2B6%29%29 Multiply the exponents.


5x=3%28x%2B6%29 Since the bases are equal, this means that the exponents are equal.


5x=3x%2B18 Distribute.


5x-3x=18 Subtract 3x from both sides.


2x=18 Combine like terms on the left side.


x=%2818%29%2F%282%29 Divide both sides by 2 to isolate x.


x=9 Reduce.


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Answer:

So the solution is x=9