SOLUTION: 3^2x=9^2x-1

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Question 176006: 3^2x=9^2x-1
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!


3%5E%282x%29=9%5E%282x-1%29

Write 9 as 3%5E2

 
3%5E%282x%29=%283%5E2%29%5E%282x-1%29

On the right side, multiply the inner exponent
2 by the outer exponent %282x-1%29

3%5E%282x%29=3%5E%282%282x-1%29%29 

Since the bases on both sides are equal and
positive and not equal to 1, we can set the
exponents equal:


2x=2%282x-1%29

2x=4x-2

-2x=-2

x=1

Check:

3%5E%282x%29=9%5E%282x-1%29

3%5E%282%2A1%29=9%5E%282%2A1-1%29

3%5E2=9%5E%282-1%29

9=9%5E1

9=9

Edwin