Logarithm Review

Rewriting Logarithms

100

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

log_1/28 = -3

200

Simplify ln(e^3x)

3x

300

Rewrite the logarithm log₃9 = 2 as an exponential.

3² = 9

400

Write 2log₂4 = 4 as an exponential 

2⁴ = 16

500

WITHOUT A CALCULATOR:

What is 10⁰? What is 10¹?

1, 10.

Natural Logarithms

100

What is the base of a natural logarithm? 

e

200

Condense the expression ln(x) + ln(4)

ln(4x)

300

Condense and simplify the following expression: 

ln(10x²) - ln(5x)

ln(2x)

400

Solve the following: 

2e^3x = 10

0.5365

500

Solve the following:

ln(x) = 3

20.0855

Expanding/Condensing

100

Expand:

log₃(xy)

log₃x + log₃y

200

Condense:

log(3x) - log(x)

log(3)

300

Completely expand:

log(5x/y)

log5 + logx - logy

400

Expand:

log(xyz)³

3logx + 3logy + 3logz

500

Condense: 

5log(x) - 7log(y)

log(x⁵/y⁷)

Solving Logarithmic Equations

100

Solve log(x) = 3

1000

200

Solve log(5x) - 3 = 2

20,000

300

log₃x = 5

243

400

Solve: log₃x + log₃9 = log₃27

3

500

Solve: ln(2x - 1) = 8

1490.98

Miscellaneous

100

What astronomical object was recently photographed for the first time? 

A black hole.

200

Which city is hosting the 2020 Summer Olympics?

Tokyo, Japan

300

What is the capital of Canada?

Ottawa

400

What is the highest grossing movie of all time?

Avatar

500

Name the four Teenage Mutant Ninja Turtles.

Leonardo, Donatello, Raphael, Michelangelo