Solving multi-step problems using non-linear equations in one variable

Solve for x using the One-to-One property.

• 3

• 16

• 10

• 8

 $e^{4x}=\ 5$  

Solve the given equation:

•  $x=\frac{\ln e}{4}$  

•  $x=\frac{4}{5}$  

•  $x=\frac{\ln\ \left(4\right)}{5}$  

•  $x=\frac{\ln\left(5\right)}{4}$  

 $\log_7\ \left(x\ +\ 4\right)\ -\ \log_{7\ }x\ =\ \log_{7\ }33$  

•  $\frac{1}{8}$  

•  $-\frac{60}{7}$  

• No solution

•  $\frac{68}{7}$  

Solve:  $\log_2\left(x\right)+\log_2\left(x-4\right)=5$   Hint: Condense, Solve, and then Check your solutions! 

• x = 8 and x = 4

• x = 8 and x = –4

• x = 8

• x = –4

Solve

• 5
• 13
• 84
• -20

log₂(3x-10)=log₂(14-x)

• 3

• 5

• 6

• 10

Solve the equation. Check for extraneous solutions. Round to the nearest hundredth, if necessary.
 $\log_3\left(-x\right)+\log_3\left(x+8\right)=2$  

What is (are) the solution(s) of the equation  $\log\left(x+3\right)+\log x=1$  

• 2, -5

• 2

• 5

• 2, 5

Solve the logarithmic equation. $\ln\left(3x\right)=\ln\left(4x+1\right)=\ln\left(1-x\right)$  

•  $x=-\frac{1}{2}$  

•  $x=2$  

•  $x=\frac{1}{2}$  

•  $x=1$