Logarithms & Exponential Functions By: Elizabeth & Ariana

Logs

100

Convert to log expression: 

2^x=8 

log₂(8)=x

200

Rewrite in log form:

5³=125

log₅125=3

300

Rewrite in exponential form:

log₄16=2

4²=16

400

Use log₂3 = 1.585 and log₂7 = 2.807 to evaluate each logarithm:

log₂3/7

4.392

500

Condense the following log:

log₅ 4 - 2 log₅ 5 

log₅ (4/25)

Solving Exponential & Log Equations

100

Solve the exponential equation:

2^x+4 = 2^5x-8

x=3

200

Solve the exponential equations with unequal bases on both sides:

2^x+2 = 8

x = log₂8-2

300

Solve the exponential inequality:

3^x <20

x < log₃20

400

Solve the log equation: 

ln(7x-4) = ln(2x+11)

x=3

500

Log5x + log (x-1) = 2 

x = 5

Graphing logs

100

Graph the following log function:

f(x) =log₃x

3^x: (-2,1/9), (-1,1/3) (0,1), (1,3), (2,9)

log₃x: (1/9,-2), (1/3,-1), (1,0), (3,1), (9,2)

200

Graph the following log function:

f(x) = log_1/3x

1/3^x = (-2,9), (-1,3), (0,1), (1,1/3), (2,1/9)

log_1/3^x = (9,-2), (3,-1), (1,0), (1/3,1), (1/9,2)

300

Graph the following log function:

y= log₅x

5^x = (-2,1/25), (-1,1/5), (0,1), (1,5), (2,25)

log₅^x = (1/25,-2), (1/5,-1), (1,0), (5,1), (25,2)

400

Graph the following log function:

log₂x

2^x = (-2,1/4), (-1,1/2), (0,1), (1,2), (2,4)

log₂^x = (1/4,-2), (1/2,-1), (1,0), (2,1), (4,2)

500

Graph the following log expression:

log_1/2x

1/2^x = (-2,4,) (-1,2), (0,1), (1,1/2), (2,1/4)

log 1/2^x = (4,-2), (2,-1), (1,0), (1/2,1) (1/4,2)

Evaluating log expressions

100

Evaluate the following expression:

log₂₅5 

x = 1/2

200

Evaluate the following expression: 

log₇ square root 7

x = 1/2

300

Evaluate the following expression:

log₄256

x = 4

400

Evaluate the following expression:

log₈1

x = 0

500

Evaluate the following expression:

log₃-9

No solution

Graph and describe transformation

100

Graph and describe the following: 

f(x)=3^x, g(x)=3^x+5

3^x = (-2,1/9) (-1,1/3), (0,1), (1,3), (2,9)

Transformation: 5 units up

200

Graph and describe the following: 

f(x)=e^-x, g(x)=e^-x+6

e^x= (-2,7.38), (-1,2.728), (0,1), (1,0.367), (2,0.135)

Transformation: Shift up 6 units

300

Graph and describe the following: 

f(x)=e^x, g(x)=e^x-1

e^x = (-2,0.135), (-1,0.3678), (0,1), (1,2.782), (2,7.389)

Transformation: Shift down 1 unit1

400

Graph and describe the following: 

f(x)=2^x, g(x)=2^x-7

2^x = (-2,1/4), (-1,1/2), (0,1), (1,2), (2,4)

Transformation: Shift right 7 units

500

Graph and describe the following: 

f(x)=(1/4)^x, g(x) - (1/4)^x-3+12

1/4^x = (-2,16), (-1,4), (0,1), (1,1/4), (2,1/16)

Transformation: Shift up 12 and Shift right 5