Question

Ok so how do you solve the following equation?

`9^x=3^(x-1)`

Thanks!

Answer 1

`x=-1`

Explanation:

`"left side "=9^x=(3^2)^x=3^(2x)`

`rArr3^(2x)=3^(x-1)larr" equation to be solved"`

Since the bases are equal. That is both 3, then we can equate the exponents.

`rArr2x=x-1rArrx=-1`

`color(blue)"As a check"`

Substitute this value into the equation and if the left side is equal to the right side then it is the solution.

`"left side "=9^-1=1/9`

`"right side "=3^-2=1/3^2=1/9`

`rArrx=-1" is the solution"`