Solve the equation.
-$\log _ { 20 } \left( x ^ { 2 } - x \right) = 1$
A) $\{ - 4,5 \}$
B) $\{ 4,5 \}$
C) $\{ - 4 , - 5 \}$
D) $\{ 1,20 \}$

Question

Quizplus · Accepted Answer

To solve the equation $\log _ { 20 } \left( x ^ { 2 } - x \right) = 1$, we first rewrite it in exponential form: $20^1 = x^2 - x$. This simplifies to $x^2 - x - 20 = 0$. Factoring this quadratic equation, we get $(x-5)(x+4) = 0$, which gives us the solutions $x = 5$ and $x = -4$. Therefore, the correct answer is $\{ - 4,5 \}$.

Solve the Equation log⁡20(x2−x)=1\log _ { 20 } \left( x ^ { 2 } - x \right) = 1log20​(x2−x)=1

Solve the Equation $\log _ { 20 } \left( x ^ { 2 } - x \right) = 1$