Solve the exponential equation algebraically.Approximate the result to three decimal places. $3 ^ { 8 x } = 2400$
A) $\frac { \ln 2400 } { 8 \ln 3 } \approx 0.018$
B) $\frac { \ln 2400 } { 8 \ln 3 } \approx 0.886$
C) $\frac { \ln 2400 } { 8 \ln 3 } \approx 0.089$
D) $\frac { \ln 2400 } { 8 \ln 3 } \approx - 0.886$
E) $\frac { \ln 2400 } { 8 \ln 3 } \approx 1.248$

Question

Solve the exponential equation algebraically.Approximate the result to three decimal places.   $3 ^ { 8 x } = 2400$  
A) $\frac { \ln 2400 } { 8 \ln 3 } \approx 0.018$
B) $\frac { \ln 2400 } { 8 \ln 3 } \approx 0.886$
C) $\frac { \ln 2400 } { 8 \ln 3 } \approx 0.089$
D) $\frac { \ln 2400 } { 8 \ln 3 } \approx - 0.886$
E) $\frac { \ln 2400 } { 8 \ln 3 } \approx 1.248$

Quizplus · Accepted Answer

To solve the equation $3^{8x} = 2400$ algebraically, we take the natural logarithm (ln) of both sides to get $8x \ln(3) = \ln(2400)$. Solving for $x$ gives $x = \frac{\ln(2400)}{8\ln(3)}$. Calculating this value gives approximately 0.886, making option B correct.

Solve the Exponential Equation Algebraically 38x=24003 ^ { 8 x } = 240038x=2400

Solve the Exponential Equation Algebraically $3 ^ { 8 x } = 2400$