Exponential/Logarithm Test Review

Log Expressions

100

Simplify the expression:  log₂ 8

What is 3?

200

Write the equation log₃(729)=6 in exponential form.

What is 3²=729 ?

300

Write the equation log(1000)=3 in exponential form.

What is 10³=1000 ?

400

Condense into one log expression. log₃(x)-2log₃(y)+3log₃(z)

What is log₃(xz³/y²)?

500

Expand the following: log₅(5x⁴y²) 

HINT: Expand then simplify.

What is 1+4log₅x+2log5y?

Exponential EQ's

100

Write the exponential equation 4⁵= 1,024 in logarithmic form.

What is log₄ 1,024=5 ?

200

Write the exponential equation 27^1/3 = 3 in logarithmic form.

What is log₂₇ 3 = 1/3 ?

300

Write the exponential equation (1/2)^-3=8 in logarithmic form.

What is log_1/28 = -3

400

Evaluate 7^-2.

What is 1/49?

500

Evaluate 81^1/2

What is 9?

Graphs of Exponential & Log Functions

100

Describe the locator point of y=log₅(x-8)+3

What is (8,3)?

200

Find the asymptote of the graph of f(x) = log(x - 1).

What is x=1 ?

300

Find the asymptote of the graph of f(x)=log(x + 2)-1.

What is x= -2 ?

400

State the domain (in interval notation) of y=log(x-5)-3.

What is (5, inf)?

500

Describe the transformations from y=log(x) to the graph of y=log(x-4)+2.

What is shift 4 units right and 2 units up?

Solving Exponential EQ's

100

Solve: 8^2x=8^(x+7)

What is x=7?

200

Solve: 25^(x-4)=5^(3x+1)

What is x=-9 ?

300

Solve: 3^x=5. Leave your answer in exact form.

What is x=log₃5?

400

Solve: 2^3+x = 15. Round to 2 decimal places.

What is 0.91?

500

Solve: 10^(2x+1) + 2 = 4 Round to two decimal places.

What is x = -0.35 ?

Solving Log EQ's

100

Solve: log x = 3

What is 1000?

200

Solve: log₃ x = 5

What is x = 243 ?

300

Solve: log (x+2) = 2 

What is x= 98?

400

Solve: log(5)+log(3x-1)=2

What is x=7?

500

Solve 

log₄(50x) - 2log₄(5) = log₄(30)

What is x=15?