`x^2 - x = log_5(25)` Solve for x or b

`x^2-x=log_5 (25)`

First, simplify the right side of the equation. To do so, factor 25.

`x^2 - x = log_5 (5^2)`

Then, apply the logarithm rule `log_b (a^m) = m * log_b (a)` .

`x^2 - x = 2 * log_5 (5)`

Take note that when the base and argument of the logarithm are the same, its resulting value is 1 `(log_b (b)=1)` .

`x^2 - x = 2 * 1`

`x^2 - x = 2`

To solve quadratic equation, one side should be zero.

`x^2 - x -2 =0`

Then, factor the left side.

`(x - 2)(x + 1)=0`

Set each factor equal to zero. And isolate the x.

`x - 2 = 0`

`x=2`

`x + 1=0`

`x=-1`

Therefore, the solution is `x = {-1,2}` .