Question

How do you solve the exponential equation `9^(2x)=27^(x-1)`?

Answer 1

`x=-3`

Explanation:

Express the equation in `color(blue)"bases of 3"`

`rArrcolor(blue)((3^2))^(2x)=color(blue)((3^3))^(x-1)`

`rArr3^(4x)=3^(3x-3)`

We can now equate the exponents.

`rArr4x=3x-3`

`rArrx=-3`