Logarithmic Functions

Logs

100

Simplify the expression 

Log(2) 32

5

200

Write log(2)25=2 in exponential Form

5²⁼²⁵

300

Write the equation log 10000=4 in exponential form

10⁴=10000

400

Solve

log₂640-log₂80

x=3

500

Solve 

log5₁₂₅⁴

x=12

Exponential Equations

100

Write 6⁵=7776 in logarithmic form

^log₆7776=5

200

Write in Logarithmic form

13²=169

log₁₃169=2

300

Write in Logarithmic form

9^3/2=27

log₉27=3/2

400

Write in Logarithmic form

9^-2=1/81

log₉1/81=-2

500

Is the graph y=log₄x increasing or decreasing.

Increasing

Solving exponential Equations

100

Solve the Following exponential equation

12^1-2x=144

x=-1/2

200

Solve the Following exponential equation

4^5x+1=16^(2x-3)

x=-7

300

Solve the Following exponential equation

log₃4x+log₃5-log₃2=4

x=8.1

400

Solve the Following exponential equation

log₆(x-1)+log₆(x+4)=2

x=5

500

Solve the Following exponential equation

8^3x+1=64^2x

x=1

Word Problems

100

A sound is 1000 times more intense than a sound you can hear. What is the measure of loudness in decibels

30dB

200

Determine the hydrogen ion concentration of a solution that has a pH of 8.2

6.31x10^-9 mL

300

Find the pH of a swimming pool with a hydrogen ion concentration of 6.1x10^-8 mol/L

pH=7.2

400

How many times more intense is the sound of a normal conversation(60 dB) compared to the sound of a whisper(30 dB)

1000 more intense

500

The Alaska earthquake of 1964 has a magnitude of 8.5 on the Richter scale. How many more times intense was the Alaska earthquake than a moderately destructive earthquake which has a magnitude of 6.0

316 times more intense

Solving Log Equations

100

Solve 

log₃(x+1)=4

x=80

200

solve 

log₄(3x+4)= log₄49

x=15

300

Solve

Log₈x+log₈(x-12)=2

x=16

400

Solve

Log(x+2)-log(x-1)=1

x=4/3

500

solve

log (root 3 x²+48x)=2/3

x=-50 or x=2