Unit 5 Review

Logarithmic or Exponential Form

Evaluating Logarithms

Logarithmic Equations

Exponential Equations

More Exponential Equations

100

Write in logarithmic form.

5³=125

log₅125=3

100

Evaluate log₁₅30

You may use your calculator. Round to the nearest hundredth if necessary.

1.26

100

Solve each equation. Round to the nearest hundredth if necessary.

log₂(5x-4)=log₂(10x-15)

x=11/5 or x=2.2

100

Solve. Round to the nearest hundredth if necessary.

15^4x+1=15^3x-2

x=-3

100

Solve. Round to the nearest hundredth if necessary.

7^x=32

x=1.78

200

Write in exponential form.

log₂16=4

2⁴=16

200

Without using a calculator, evaluate

log₂8

200

Solve each equation. Round to the nearest hundredth if necessary.

log₃4+log₃(x+2)=log₃62

x=13.5 or x=27/2

200

Solve. Round to the nearest hundredth if necessary.

4^2x_*4⁵=4¹⁰

x=2.5 or x=5/2

200

Solve. Round to the nearest hundredth if necessary.

8^x-2=13

x=3.23

300

Write in logarithmic form.

3^5x=20

log₃20=5x

300

Without using a calculator, evaluate log₂(-3).

Explain how you know.

No solution.

300

Solve each equation. Round to the nearest hundredth if necessary.

log₄(4a-2)=2

a=4.5 or a=9/2

300

Solve. Round to the nearest hundredth if necessary.

4^3x=32

x=5/6 or x=0.83

300

Solve. Round to the nearest hundredth if necessary.

3^5x+1=37

x = 0.65

400

Write in exponential form.

log₅36=x-2

5^x-2=36

400

Evaluate without using a calculator,

log₂(1/2)

-1

400

Solve each equation. Round to the nearest hundredth if necessary.

log₈(3-2x)=1/3

x=1/2 or x=0.5

400

Solve. Round to the nearest hundredth if necessary.

27=(1/9)^x+3

x=-4.5 or x= -9/2

400

Solve. Round to the nearest hundredth if necessary.

3 _*10^x+ 4=52

x=1.20

500

Write in exponential form.

log 100=2

10²=100

500

Without using a calculator, evaluate

log₈₁9

1/2

500

Solve each equation. Round to the nearest hundredth if necessary.

log(2x-8) - log2=2

x=104

500

Solve. Round to the nearest hundredth if necessary.

(1/2)^a_*4^2a= 8

a=1

500

Solve. Round to the nearest hundredth if necessary.

5 _*13^x-2 - 3 = 42

x=2.86