Solve the equation and express the solution in exact form.
-$$\ln ( 2 x - 1 ) + \ln ( x - 5 ) = \ln 5$$
A) $\varnothing$
B) $\left\{ 5 , \frac { 5 } { 2 } \right\}$
C) $\left\{ \frac { 11 } { 2 } \right\}$
D) $\left\{ 0 , \frac { 11 } { 2 } \right\}$

Question

Quizplus · Accepted Answer

Combine the logarithms: $\ln((2x-1)(x-5)) = \ln 5$. Set the arguments equal: $(2x-1)(x-5) = 5$. Solve the quadratic equation: $2x^2 - 11x + 5 = 0$. The solution is $x = \frac{11}{2}$, which is valid since it satisfies the domain of the original logarithmic expressions.

Solve the Equation and Express the Solution in Exact Form ln⁡(2x−1)+ln⁡(x−5)=ln⁡5\ln ( 2 x - 1 ) + \ln ( x - 5 ) = \ln 5ln(2x−1)+ln(x−5)=ln5

Solve the Equation and Express the Solution in Exact Form $\ln ( 2 x - 1 ) + \ln ( x - 5 ) = \ln 5$