Exponential and Logarithmic Functions

Exponential Function

100

Determine whether the equation represents exponential growth, exponential decay, or neither,
y=220e^x

 Exponential Growth

200

ln (e)= 

1

300

Determine whether the equation represents continuous growth, continuous decay, or neither, y=3742(e)^.75t

What is continuous growth?

400

Determine whether the equation represents continuous growth, continuous decay, or neither, y=2.25(e)^-2t

 decay

500

Write e³=12 in logarithmic form

ln(12)=3

Logarithmic Function

100

Rewrite the equation log_y(x)=−11 into exponential form

What is y^-11=x?

200

Rewrite c^d= k into logarithmic form

What is log_c(k)= d?

300

Solve for x in the equation log(x)=3

What is x=1000?

400

Solve for x in the equation log₉(x)=1/2

What is x=3?

500

Evaluate the base b logarithmic equation when the function is 6log₈(4)

What is 4?

Logarithmic Properties

100

Expand this logarithm, log_b(7x⋅2y)

What is log_b(2)+log_b(7)+log_b(x)+log_b(y)?

200

Condense the equation into a single logarithm, log_b(28)−log_b(7)

What is log_b(4)?

300

Expand the logarithm as much as possible, log(x¹⁵y¹³/z¹⁹)

What is 15log(x) + 13log(y) - 19log(z)?

400

Condense the expression to a single logarithm,    log(x)−1/2log(y)+3log(z)

What is log(xz^3/√y)?

500

Evaluate the following expression without using a calculator, 6log₈(2)+log₈(64)/3log₈(4)

 3

Exponential and Logarithmic Equations

100

Use like bases to solve the exponential equation, 64e^3x=16

 x=-0.46

200

Use logarithms to solve,
e^r+10−10=−42

What is No Solution?

300

Use logarithms to solve, −8⋅10^p+7−7=−24

What is p= log(17/8) - 7?

400

Use logarithms to solve,
−6e^9x+8+2=−74

What is x= ln(38/3)-8/9?

500

Use definition of logarithm to solve the equation,
4+log₂(9k)=2

What is k= 1/36?