SOLUTION: Solve for x if x:3^2x = 9^2x-1

Question 1177146: Solve for x if x:3^2x = 9^2x-1
Found 2 solutions by greenestamps, MathLover1:
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Rewrite 9 as 3^2 to make the bases the same:

This is a quadratic equation with "3^(2x)" as the "variable". To make it easier to solve, let y=3^(2x), so that 3^(4x) = y^2:

That quadratic does not factor; using the quadratic formula gives us

Those values are one positive and one negative. We can ignore the negative root, because y=3^(2x) is never negative. So

A calculator shows the value to be 0.219 to 3 decimal places.

Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

............if base same, exponents are same too

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