Solve the equation. Give the exact solution or solutions.
-$\log (2 x-1)=\log 1-\log (x-1)$
A) $\left\{0, \frac{3}{2}\right\}$
B) $\left\{\frac{3}{2}\right\}$
C) $\varnothing$
D) $\left\{1, \frac{1}{2}\right\}$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, we can combine the right side as a single logarithm: $\log(2x - 1) = \log\left(\frac{1}{x-1}\right)$. For two logarithms to be equal, their arguments must be equal, leading to $2x - 1 = \frac{1}{x-1}$. Solving this equation for $x$ gives $x = \frac{3}{2}$ as the only solution that satisfies the original equation.

Solve the Equation log⁡(2x−1)=log⁡1−log⁡(x−1)\log (2 x-1)=\log 1-\log (x-1)log(2x−1)=log1−log(x−1) A) {0,32}\left\{0, \frac{3}{2}\right\}{0,23​} B) {32}\left\{\frac{3}{2}\right\}{23​}

Solve the Equation $\log (2 x-1)=\log 1-\log (x-1)$ A) $\left\{0, \frac{3}{2}\right\}$ B) $\left\{\frac{3}{2}\right\}$