Solve the following graphically. If necessary, round answers to the nearest thousandth.
-The exact solution to an exponential equation such as $2 ^ { x } = 3$ can be expressed in three forms: $\log _ { 2 } 3 , \frac { \log 3 } { \log 2 }$, or $\frac { \ln 3 } { \ln 2 }$. Give the exact solution to the following exponential equation in three forms. $3 ^ { x } = 11$
A) $\log _ { 11 } 3 ; \frac { \log 11 } { \log 3 } ; \frac { \ln 11 } { \ln 3 }$

B) $\log _ { 3 } 11 ; \frac { \log 3 } { \log 11 } ; \frac { \ln 3 } { \ln 11 }$

C) $\log _ { 11 } 3 ; \frac { \log 3 } { \log 11 } ; \frac { \ln 3 } { \ln 11 }$

D) $\log _ { 3 } 11 ; \frac { \log 11 } { \log 3 } ; \frac { \ln 11 } { \ln 3 }$

Question

Solve the following graphically. If necessary, round answers to the nearest thousandth.
-The exact solution to an exponential equation such as $2 ^ { x } = 3$ can be expressed in three forms: $\log _ { 2 } 3 , \frac { \log 3 } { \log 2 }$, or $\frac { \ln 3 } { \ln 2 }$. Give the exact solution to the following exponential equation in three forms. $3 ^ { x } = 11$
A) $\log _ { 11 } 3 ; \frac { \log 11 } { \log 3 } ; \frac { \ln 11 } { \ln 3 }$

B) $\log _ { 3 } 11 ; \frac { \log 3 } { \log 11 } ; \frac { \ln 3 } { \ln 11 }$

C) $\log _ { 11 } 3 ; \frac { \log 3 } { \log 11 } ; \frac { \ln 3 } { \ln 11 }$

D) $\log _ { 3 } 11 ; \frac { \log 11 } { \log 3 } ; \frac { \ln 11 } { \ln 3 }$

Quizplus · Accepted Answer

The correct way to express the solution to $3^x = 11$ in logarithmic form is by taking the logarithm of both sides, resulting in $x = \log_3 11$. This can also be converted to the base 10 or natural logarithm (base e) forms using the change of base formula, resulting in $x = \frac{\log 11}{\log 3}$ or $x = \frac{\ln 11}{\ln 3}$, respectively.

Solve the Following Graphically 2x=32 ^ { x } = 32x=3

Solve the Following Graphically $2 ^ { x } = 3$