Solve the exponential equation algebraically.Approximate the result to three decimal places. $6 ^ { x } + 8 = 57$
A) $\frac { \ln 49 } { \ln 6 } \approx 2.172$
B) $\frac { \ln 49 } { \ln 6 } \approx - 0.460$
C) $\frac { \ln 49 } { \ln 6 } \approx 0.514$
D) $\frac { \ln 49 } { \ln 6 } \approx 0.460$
E) $\frac { \ln 49 } { \ln 6 } \approx - 2.172$

Question

Solve the exponential equation algebraically.Approximate the result to three decimal places.   $6 ^ { x } + 8 = 57$  
A) $\frac { \ln 49 } { \ln 6 } \approx 2.172$
B) $\frac { \ln 49 } { \ln 6 } \approx - 0.460$
C) $\frac { \ln 49 } { \ln 6 } \approx 0.514$
D) $\frac { \ln 49 } { \ln 6 } \approx 0.460$
E) $\frac { \ln 49 } { \ln 6 } \approx - 2.172$

Quizplus · Accepted Answer

First, solve the equation $6^x + 8 = 57$ by subtracting 8 from both sides to get $6^x = 49$. Taking the natural logarithm (ln) of both sides gives $x \ln 6 = \ln 49$, which simplifies to $x = \frac{\ln 49}{\ln 6}$. Calculating this value gives approximately 2.172.

Solve the Exponential Equation Algebraically 6x+8=576 ^ { x } + 8 = 576x+8=57

Solve the Exponential Equation Algebraically $6 ^ { x } + 8 = 57$