Solve the equation.
-$\ln (5 x-6)=\ln 36-\ln (x-6)$
A) $\varnothing$
B) $\left\{6, \frac{6}{5}\right\}$
C) $\left\{\frac{36}{5}\right\}$
D) $\left\{0, \frac{36}{5}\right\}$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, we can combine the right side of the equation: $\ln(36) - \ln(x-6) = \ln\left(\frac{36}{x-6}\right)$. Therefore, the equation becomes $\ln(5x-6) = \ln\left(\frac{36}{x-6}\right)$. Since the natural log function is one-to-one, $5x-6 = \frac{36}{x-6}$. Solving this equation for $x$ gives $x = \frac{36}{5}$, which is the only solution that satisfies the original equation.

Solve the Equation ln⁡(5x−6)=ln⁡36−ln⁡(x−6)\ln (5 x-6)=\ln 36-\ln (x-6)ln(5x−6)=ln36−ln(x−6) A) ∅\varnothing∅ B) {6,65}\left\{6, \frac{6}{5}\right\}{6,56​}

Solve the Equation $\ln (5 x-6)=\ln 36-\ln (x-6)$ A) $\varnothing$ B) $\left\{6, \frac{6}{5}\right\}$