6.62pc MQ Solving Exponential Equations using Logs

How would you begin to solve for x in this exponential equation?

  $3^{x-1}=24$  

Select 3 appropriate beginning steps. 

•  $\log\left(3^{x-1}\right)=\log\left(24\right)$  

•  $\log_3\left(3^{x-1}\right)=\log_3\left(24\right)$  

•  $\ln\left(3^{x-1}\right)=\ln\left(24\right)$  

•  $\frac{3^{x-1}}{3}=\frac{24}{3}$  

Which of the following is NOT a correct step toward the solving of this exponential equation?

  $2e^{3x}=16$  

•  $\frac{2e^{3x}}{2}=\frac{16}{2}$  

•  $\ln\left(e^{3x}\right)=\ln\left(8\right)$  

•  $3x=\ln\left(8\right)$  

•  $x=\ln\left(\frac{8}{3}\right)$  

Solve for x in the exponential equation.

 $7^x=12$ 


Round your answer to the nearest hundreth.

Solve for x in the exponential equation.

 $4^{2x}=32$  

Round your answer to the nearest hundreth.

Solve for x in the exponential equation.

 $4^x-5=12$  

Round your answer to the nearest hundreth.

Solve for x in the exponential equation.

 $8^{x+1}=3$  

Round your answer to the nearest hundreth.

Solve for x in the exponential equation.

 $10^{3x}-1=5$  

Round your answer to the nearest hundreth.

Solve for x in the exponential equation.

 $6-e^{12x}=5.2$  

Round your answer to the nearest hundreth.

Solve for x in the exponential equation.

 $5e^{6x+3}=0.1$  

Round your answer to the nearest hundreth.

Solve for x in the exponential equation.

 $e^{x+6}+5=1$  

Round your answer to the nearest hundreth.

•  $x+6=\ln6,\ \ Therefore\ x=-4.21$  

•  $x+6=\ln\left(4\right),\ \ Therefore\ x=-4.61$  

•  $x+6=\ln\left(-4\right),\ \ Therefore\ no\ solution$  

•  $\ln e^{x+11}=1,\ \ Therefore\ x=-10$