Exponential & Logarithm Functions

Exponential Functions

100

Convert y=3^x into logarithmic form

log₃y=x

200

What is the domain of the function y=2(3)^x

All Real Numbers

300

What is the range of y=2(3)^x

[0, infinity)

400

What is the equation of the asymptote of the function y=2(3)^x

y=0

500

What is the equation of the asymptote of y=-3(4)^x+5-2

y=-2

Logarithmic Functions

100

Convert log₄x=y into exponential form

4^y=x

200

What is the domain of log₄(x)

(0, infinity)

300

What is the range of y=log₄(x)

All real numbers

400

What is the equation of the asymptote of the function y=log₄(x)

x=0

500

Without using a calculator, evaluate the following logarithm: log₃27^1/2

3/2

Logs Properties

100

Finish the log property: log(a)+log(b)=

log(ab)

200

Finish the log property log(a/b)=

log(a)-log(b)

300

Expand using log properties: log(x²y³)

2log(x)+3log(y)

400

Condense using log properties: log(x)-log(y)-log(z)

log(x/(yz))

500

Condense using log properties: 1/2(log(a)-log(b))

log(a/b)^1/2

Solving Exponential Equations

100

Solve for x: 5^x=5⁶

x=6

200

Solve for x: 5^x=25⁵

x=10

300

Solve for x: 5^x+3=1/25

x=-5

400

Solve for x: 5^4x=65

0.65

500

Solve for x: 4e^x-1=12

1.18

Solving Logarithmic Equations

100

Solve for x: log(x)=log(4)

x=4

200

Solve for x: log(x²)=log(25)

x=5, 

x=-5 is extraneous solution

300

Solve for x: log(x)+log(5)=log(100)

x=20

400

Solve for x: log₄(x-8)=2

x=24

500

Solve for x: 5ln(x²)=24

x= 11.02, -11.02