Logarithmic and Exponential Functions

Solve the equation

 $3^x=2000$  

• x=6.92

• x=6.93

• x=6.91

• x=7

Tags

CCSS.HSF.LE.A.4

Solve the following equation

 $4e^{3x}=950$  

• x=5.47

• x=1.82

• x=237.5
  

• x=79.2

Tags

CCSS.HSF.LE.A.4

Use logarithms to solve the equation

 $3^{\left(5-x\right)}=2^{\left(5+x\right)}$  

• x=2.26

• x=1.13

• x=0.13

• There is no solution to this equation
  

Solve the following equation.
Select all the options that apply to the correct solution.

 $\left(0.85\right)^n\times20000=5000$  

•  $n=\frac{\lg0.5}{\lg0.85}$  

•  $n=\log_{0.85}0.5$  

•  $n=\frac{\ln0.5}{\ln0.85}$  

•  $n=\frac{\log\left(-0.5\right)}{\log\left(-0.85\right)}$  

Use appropriate substitution to solve the following equation.

 $e^{2x}-5e^x+6=0$ 

• x=0.693,  x=1.099
  

• x=2,  x=3
  

• x=1.5,  x=0.667
  

• x=0.712,  x=2.141
  

Given that

 $\log_apq=9$  and  $\log_ap^2q=15$ 
Select the following statements which are true.

•  $\log_ap=6$  

•  $\log_aq=3$  

•  $\log_pa+\log_qa=0.5$  

•  $\log_ap-\log_aq=6$