Exponential and Logarithmic Review

Basic Exponential Functions

100

What is the y-intercept of the following exponential function?

f(x)=5(2)^x

(0, 5)

200

Does the exponential function below show exponential growth or decay?

f(x)=1/2(5)^x

Exponential Growth

300

What is the y-intercept of the following exponential function?

f(x)=-(1/2)^x

(0, -1)

400

Does the exponential function below show exponential growth or decay?

f(x)=4(2/3)^x

Exponential Decay

500

What is the asymptote of the following exponential function.

f(x)=2(3)^(x-5)+8

y=8

Evaluate

100

log₅5

1

200

log₃81

4

300

log₄(1/16)

-2

400

log₂₇3

1/3

500

1/2log100

1

Graphs of Exponential Functions

100

Describe the transformations that take place to get the graph of g(x) from the parent function f(x).

f(x)=3^x

g(x)=3^(x+2)-5

Shifted 2 units left and 5 units down

200

Describe the transformations that take place to get the graph of g(x) from the parent function f(x).

f(x)=e^x

g(x)=-2e^x

Reflected across the x-axis and vertically stretched by a factor of 2.

300

Describe the transformations that take place to get the graph of g(x) from the parent function f(x).

f(x)=(1/2)^x

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

Reflected across the x-axis, stretched by a factor of 3, shifted 4 units right, and shifted 5 units up.

400

Graphing! Graph the function g(x) and its parent function f(x) on the same coordinate plane.

f(x)=2^x

g(x)=2^(x+3)-5

Check students' graph.

500

Graphing! Graph the function g(x) and its parent function f(x) on the same coordinate plane.

f(x)=e^x

g(x)=-1/2(e)^x+2

Check students' graphs.

Common Logarithm

100

Without a calculator, evaluate the following logarithm.

log100

2

200

Without a calculator, evaluate the following logarithm.

log (1/1000)

-3

300

Write the exponential statement that corresponds to the logarithmic statement below.

log1=0

10^0=1

400

Write the exponential statement that corresponds to the logarithmic statement below.

log10000=4

10^4=10000

500

Write the logarithmic statement that corresponds to the exponential statement below.

10^-3=1/1000

log(1/1000)=-3

Logarithm Properties

100

Use properties of logarithms to condense the following logarithmic expression into a single logarithm.

log5-log9

log(5/9)

200

Use properties of logarithms to condense the following logarithmic expression into a single logarithm.

10log5+log8

log(5^10*8)

300

Use properties of logarithms to expand the following logarithmic expression.

log(4^5*3)

5log4+log3

400

Use properties of logarithms to expand the following logarithmic expression.

log(5/12)^3

3log5-3log12

500

Use properties of logarithms to condense/expand the following logarithmic expression.

log((9^3*6)/4^5)

3log9+log6-5log4