Solve.
-$\ln \left(x^{2}+9 x-49\right)=\ln (5 x-4)$
A) $\{5\}$
B) $\varnothing$
C) $\{-9,5\}$
D) $\{5,9\}$

Question

Quizplus · Accepted Answer

Since both sides of the equation are logarithms with the same base, we can set the arguments equal to each other: $x^2 + 9x - 49 = 5x - 4$. Simplifying gives $x^2 + 4x - 45 = 0$, which factors to $(x + 9)(x - 5) = 0$. Thus, $x = -9$ or $x = 5$. However, substituting $x = -9$ back into the original equation gives a negative argument for the logarithm, which is not valid. Therefore, the only solution is $x = 5$.

Solve - ln⁡(x2+9x−49)=ln⁡(5x−4)\ln \left(x^{2}+9 x-49\right)=\ln (5 x-4)ln(x2+9x−49)=ln(5x−4) A) {5}\{5\}{5} B) ∅\varnothing∅ C) {−9,5}\{-9,5\}{−9,5} D) {5,9}\{5,9\}{5,9}

Solve
- $\ln \left(x^{2}+9 x-49\right)=\ln (5 x-4)$ A) $\{5\}$ B) $\varnothing$ C) $\{-9,5\}$ D) $\{5,9\}$