SOLUTION: 7^x^2-15=49^x

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Question 248608: 7^x^2-15=49^x
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Unless an exponent is just a single number or variable, please put parentheses around it. I can't tell if the left side is:
7%5E%28x%5E2%29-15, %287%5Ex%29%5E2-15 or 7%5E%28x%5E2-15%29
These are all different and will have different solutions. So I really can't help you much until I know which is correct.

But I can say that the solution will probably take advantage of the fact that 49 is a power of 7:
49%5Ex+=+%287%5E2%29%5Ex+=+7%5E%282x%29
(The last part comes from the rule for exponents: %28a%5Ep%29%5Eq+=+a%5E%28p%2Aq%29)

If the left side is 7%5E%28x%5E2-15%29, then the problem is easier than the other two possibilities:
7%5E%28x%5E2-15%29+=+7%5E%282x%29
With both the left side and the right side being a powers of 7, the exponents must be equal:
x%5E2-15+=+2x
This is now a quadratic equation. So we'll get one side equal to zero (by subtracting 2x):
x%5E2-2x-15+=+0
Factor:
%28x-5%29%28x%2B3%29+=+0
Use the Zero Product Property:
x-5+=+0 or x%2B3+=+0
Solve:
x+=+5 or x+=+-3