Logarithmic Functions Review Jeopardy

Express Logarithms and Exponential Expressions

100

Write the exponential expression in logarithmic form:

4³ = 64

log_bx = y

log₄64 = 3

200

Write the logarithm as an exponential expression: 

log_x(128) = 7

x⁷ = 128

300

Write the exponential expression as a logarithm: 

7^3x = 12 

7^3x = 12 

3x = log₇12

x = (log₇12)/3

400

Write the logarithm as an exponential expression: 

x = (log₆24)/3

x = (log₆24)/3

3(x) = log₆24

6^3x = 24

500

Write the logarithm as an exponential expression: 

x = (log₈120)/-6

x = (log₈120)/-6

-6(x) = log₈120

8^-6x = 120

Properties and Laws of Log and Change of Base

100

Use the properties and laws of log to answer:

log₂₄16 + log₂₄36

A: x = 2

200

Use the properties and laws of log to answer:

log₅125⁴

A: x = 12

300

Use the properties and laws of log to answer:

log₃√45 - log₃√5 + log₃√25

A: log₃15

400

Rewrite logarithm expression: 

log₈ ((⁶√r⁵ • s³)/t²)

(hint: log_ax)

A: 5/6log₈r + 3log₈s - 2log₈t

500

Given log₁₂3 = 0.4421 and log₁₂7 = 0.7831, solve for the exact value of: 

log₁₂(81/49) + log₁₂16807 - log₁₂441

A: 1.6673

Solving Equations

100

Solve the following equation:

12209 = 2.5ⁿ

A: n=10.27

200

Solve the following equation:

243^q = 27^-3q+1

A: q = 3/14

300

Solve the following equation:

log₃(x-2) + log₃(x) = 1

A: x=3

x ≠ -1 <--- extraneous root, cannot be true

400

Solve the following equation:

3log₂x - log₂x = 8

A: x=16 

x≠-16 <---- extraneous root, cannot be true

500

Solve the following equation:

1 - log(x-4) - log(x+5) = 0

A: x=-6 and 5