Calculus of a Single Variable, Chapter 5, 5.5, Section 5.5, Problem 23

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} .