Solving Exponential Equations (Using Logs)

Solve:  $7^x=12$ 
Round your answer to two decimal places.

Solve:  $10^{3x}-1=5$  
Round your answer to two decimal places.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Solve:  $3^{x+5}=15$  
Round your answer to two decimal places.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Solve:  $2e^{3x}=16$  
Select the first incorrect step in solving this equation.

• STEP 1: $\frac{2e^{3x}}{2}=\frac{16}{2}$  

• STEP 2: $\ln\left(e^{3x}\right)=\ln\left(8\right)$  

• STEP 3: $3x=\ln\left(8\right)$  

• STEP 4: $x=\ln\left(\frac{8}{3}\right)$  

Solve:  $3^{x-1}=24$  
Select all possible ways in which you can start solving this equation.

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

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

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

•  $\frac{3^{x-1}}{3}=\frac{24}{3}$  

 $4^{2x}=32$  

Select all equations that are equivalent to the equation given above.

•  $2^{4x}=2^5$  

•  $8^x=32$  

•  $16^x=32$  

•  $\left(4\right)^{2x}=2\cdot\left(4\right)^2$  

Tags

CCSS.HSA.CED.A.1

CCSS.HSF.LE.A.2

What is the solution of $3e^{2x}+1=5$  ?

•  $x\approx0.131$  

•  $x\approx0.187$  

•  $x\approx0.151$  

•  $x=0.144$  

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.REI.D.11

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Solve $82\cdot\left(3^{2x-4}\right)-110=557$ .  Round your answer to the nearest tenth.  

• 1.8

• 2.9

• 3.5

• 3.9

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.4

Solve $4\cdot\left(3^x\right)=26$  for x.

• 0.3

• 1.7

• 1.3

• 2.2

Solve $3\cdot\left(2\right)^{x+3}-1=8$ .  Round your answer to two decimal places, the hundredths place.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.4