Solve the equation.
-$\log _ { 72 } \left( x ^ { 2 } - x \right) = 1$
A) $\{ - 8,9 \}$
B) $\{ 1,72 \}$
C) $\{ - 8 , - 9 \}$
D) $\{ 8,9 \}$

Question

Quizplus · Accepted Answer

To solve the equation $\log_{72}(x^2 - x) = 1$, we rewrite it in exponential form: $72^1 = x^2 - x$. This simplifies to $72 = x^2 - x$. Rearranging gives $x^2 - x - 72 = 0$. Factoring this quadratic equation, we find $x^2 - 9x + 8x - 72 = 0$, which simplifies to $x(x - 9) + 8(x - 9) = 0$, leading to $(x + 8)(x - 9) = 0$. Thus, the solutions are $x = -8$ and $x = 9$, making the correct answer $\{-8, 9\}$.

Solve the Equation log⁡72(x2−x)=1\log _ { 72 } \left( x ^ { 2 } - x \right) = 1log72​(x2−x)=1

Solve the Equation $\log _ { 72 } \left( x ^ { 2 } - x \right) = 1$