Solving Exponential and Logarithmic Equations

Solve the equation. Check for extraneous solutions.
 $\log_2x+\log_2\left(x-3\right)=2$  

Tags

CCSS.HSA.REI.A.2

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Solve the equation. Check for extraneous solutions. Round to the nearest hundredth, if necessary.
 $\ln\ x+\ln\ \left(x+4\right)=3$  

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.A.2

The length l (in centimeters) of a scalloped hammerhead shark can be modeled by the function $l=266-219e^{-0.05t}$  

 − where t is the age (in years) of the shark. How old is a shark that is 200 centimeters long? Round to the nearest tenth.

Fifty grams of radium are stored in a container. The amount R (in grams) of radium present after t years can be modeled by $R=50e^{-0.00043t}$ . After how many years will only 20 grams of radium be present?  Round to the nearest tenth.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.SSE.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

Solve the equation.
 $\log_2\left(3x+12\right)=4$ 

Solve the equation.
 $\log_2\left(x^2-2x+1\right)=4$ 

Solve the equation.
 $\log_3\left(x^2+x+7\right)=3$ 

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Solve the equation. Check for extraneous solutions. Round to the nearest thousandth, if necessary.
 $\log_2\left(x+2\right)+\log_2\left(x+5\right)=4$  

Tags

CCSS.HSA.REI.A.2

CCSS.HSF.BF.B.5

Solve the equation. Check for extraneous solutions. Round to the nearest hundredth, if necessary.
 $\log_52x^2+\log_58=2$  

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