Solve the equation. Give the solution to three decimal places.
-$5^{-5 x-3}=24$
A) $\{-0.995\}$
B) $\{--0.205\}$
C) $\{-0.914\}$
D) $\{-1.560\}$

Question

Quizplus · Accepted Answer

To solve the equation $5^{-5x-3} = 24$, we first take the logarithm of both sides. Using the natural logarithm, we get $\ln(5^{-5x-3}) = \ln(24)$. Applying the logarithm power rule, this becomes $(-5x-3) \ln(5) = \ln(24)$. Solving for $x$, we get $x = \frac{-\ln(24) - 3\ln(5)}{-5\ln(5)}$, which simplifies to approximately $x = -0.995$.

Solve the Equation 5−5x−3=245^{-5 x-3}=245−5x−3=24 A) {−0.995}\{-0.995\}{−0.995} B) {−−0.205}\{--0.205\}{−−0.205} C) {−0.914}\{-0.914\}{−0.914} D) {−1.560}\{-1.560\}{−1.560}

Solve the Equation $5^{-5 x-3}=24$ A) $\{-0.995\}$ B) $\{--0.205\}$ C) $\{-0.914\}$ D) $\{-1.560\}$