Solve the equation. Give an approximate solution to four decimal places.
-$5 ^ { 3 x } = 4.1$
A) $2.7987$
B) $0.2922$
C) $0.2569$
D) $2.6301$

Question

Quizplus · Accepted Answer

To solve the equation $5^{3x} = 4.1$, take the logarithm of both sides. Using the natural logarithm, $\ln(5^{3x}) = \ln(4.1)$. Applying the logarithm power rule, $3x \ln(5) = \ln(4.1)$. Solving for $x$, $x = \frac{\ln(4.1)}{3\ln(5)}$. Calculating this gives $x \approx 0.2922$.

Solve the Equation 53x=4.15 ^ { 3 x } = 4.153x=4.1

Solve the Equation $5 ^ { 3 x } = 4.1$