Question

3^2x-3^x-24=0

Could you also teach me the process in answering it?

Answer 1

Let 3^x = y

==> 3^2x - 3^x - 24 =0
= y^2 - y - 24 = 0

solve for y using quadratic equation.
You will get 2 answers for y, one positive, the other negative.

But 3^x = y,
thus equate 3^x = y for both answers of y.

Use log on both sides, and then solve for x.

You will see, when y is negative, you wont be able to use log, therefore, we neglect the negative.

Hope this helps.