Solve the equation.
-$\log _ { 35 } ( x - 2 ) = 1 - \log _ { 35 } x$
A) $\{ 5 \}$
B) $\{ - 7 \}$
C) $\{ 7 \}$
D) $\{ - 5 \}$

Question

Quizplus · Accepted Answer

To solve the equation, use the property of logarithms: $\log_b a - \log_b c = \log_b \frac{a}{c}$. Rewrite the equation as $\log_{35} (x - 2) + \log_{35} x = 1$, which simplifies to $\log_{35} \frac{x-2}{x} = 1$. This implies $\frac{x-2}{x} = 35^1 = 35$. Solving $\frac{x-2}{x} = 35$ gives $x = 7$.

Solve the Equation log⁡35(x−2)=1−log⁡35x\log _ { 35 } ( x - 2 ) = 1 - \log _ { 35 } xlog35​(x−2)=1−log35​x

Solve the Equation $\log _ { 35 } ( x - 2 ) = 1 - \log _ { 35 } x$