Question

I have to solve the equation by finding a common base.

9^(x2-1)= 1/27^x

Do i cross multiply and solve for x?

Answer 1

You need to figure out the same base for both sides.

In other words: 9 = 3^2 and 1/27 = 3^-3

Note: I'm using ^ to mean raised to the power of.

Therefore, we now have this:

(3^2)^(x^2 - 1) = (3^-3)^(x)

Since 3 is now the common base, work with the exponents only.

2(x^2-1) = -3x
2x^2-2 = -3x

Set the equation equal to 0:
2x^2 + 3x - 2 = 0

Try to factor:
(2x - 1)(x + 2) = 0

Now set each factor equal to 0:
2x - 1 = 0; x = 1/2
x + 2 = 0; x = -2

Those are your two possible solutions.

Check those answers with the original equation. It always helps to check your work!

I hope this helps.