SOLUTION: Solve the equation: (4^2-x)(16^x+1)=64 FYI - The 2-x and x+1 the exponents.

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Question 142061: Solve the equation: (4^2-x)(16^x+1)=64
FYI - The 2-x and x+1 the exponents.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%284%5E%282-x%29%29%2816%5E%28x%2B1%29%29=64 Start with the given equation


%284%5E%282-x%29%29%28%284%5E2%29%5E%28x%2B1%29%29=64 Rewrite 16 as 4%5E2


%284%5E%282-x%29%29%284%5E%282%28x%2B1%29%29%29=64 Use the identity %28x%5Ey%29%5Ez=x%5E%28y%2Az%29 to rewrite the second term on the left side


%284%5E%282-x%29%29%284%5E%282%28x%2B1%29%29%29=4%5E3 Rewrite 64 as 4%5E3


%284%5E%282-x%29%29%284%5E%282x%2B2%29%29=4%5E3 Distribute 2 to x%2B1 to get 2x%2B2


4%5E%28%282-x%29%2B%282x%2B2%29%29=4%5E3 Multiply the terms on the left side by adding the exponents


4%5E%282-x%2B2x%2B2%29=4%5E3 Remove the parenthesis


4%5E%28x%2B4%29=4%5E3 Combine like terms



x%2B4=3 Since the bases are equal, this means that the exponents are equal



x=3-4Subtract 4 from both sides



x=-1 Combine like terms on the right side

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Answer:
So our answer is x=-1