Solve the exponential equation algebraically.Approximate the result to three decimal places. $6 ^ { - 5 x } = 0.50$
A) $- \frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx 0.072$
B) $\frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx 0.517$
C) $- \frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx 0.387$
D) $- \frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx 0.077$
E) $- \frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx - 0.077$

Question

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ $6 ^ { - 5 x } = 0.50$ ​
A) $- \frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx 0.072$
B) $\frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx 0.517$
C) $- \frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx 0.387$
D) $- \frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx 0.077$
E) $- \frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx - 0.077$

Quizplus · Accepted Answer

To solve the equation $6^{-5x} = 0.50$, we take the natural logarithm on both sides, resulting in $-5x \ln(6) = \ln(0.50)$. Solving for $x$ gives $x = -\frac{\ln(0.50)}{5\ln(6)}$. Calculating this value gives approximately 0.077, making option D correct.

Solve the Exponential Equation Algebraically 6−5x=0.506 ^ { - 5 x } = 0.506−5x=0.50

Solve the Exponential Equation Algebraically $6 ^ { - 5 x } = 0.50$