MODULE 6 JEOPARDY

Switching Between Forms

100

Write log₂(8)=3 in exponential form.

2³=8

200

Write 4³ = 64 in logarithmic form.

log₄(64) = 3

300

Write the following common logarithm in exponential form:

log(6) = y

10^y = 6

400

Write ln(1) = 0 in exponential form

e⁰ = 1

500

Write e³ ≈ 20.09 in logarithmic form.

ln(20.09) ≈ 3

Logarithmic Properties

100

Simplify log₄(8) + log₄(2) using logarithmic properties.

log₄(16)

200

State the property that is used:

log₅(30) - log₅(3) = log₅(10)

Quotient Property of Logarithms

300

Expand log₉( (2/7)³ ) COMPLETELY using logarithmic properties.

3log₉(2) - 3log₉(7)

400

Expand log₆( (4x)² / 11 ) COMPLETELY using logarithmic properties.

2log₆(4) + 2log₆(x) - log₆(11)

500

Condense 2log₈(x) - log₈(y + 1) + 3log₈(z) into one logarithm.

log₈( (x²z³) / (y + 1) )

Common Logs

100

What is the base for a common logarithm?

10

200

Evaluate the following common logarithm:

log(1000)

3

300

Write log₅(22) in terms of common logarithms.

( log(22) ) / ( log(5) )

400

Evaluate:

log( 1/100 )

-2

500

Combine 2log₇(3) + log₇(4) into one logarithm, THEN write it in terms of common logarithms.

( log(36) ) / ( log(7) )

Natural Logs

100

What is the base for a natural logarithm?

e

200

How do we represent the natural logarithm?

ln(___)

300

Evaluate the following natural logarithm:

ln(e⁴)

4

400

Find the value of x that makes the equation true:

ln( 2x + 3 ) = ln( -3x + 8 )

x = 1

500

Condense 3ln(16) - 4ln(8) into one logarithm and evaluate COMPLETELY using logarithmic properties.

0

Solving Equations/Inequalities

100

Find the value of x that makes the equation true.

log₃(2x + 1) = log₃(x + 7)

x = 6

200

Solve:

log₄(x) = 3/2

x = 8

300

Solve:

log(x² + x) = log(6)

x = -3

x = 2

400

Solve:

2ln( x + 1 ) < 8

x < e⁴ - 1

500

Solve:

7²ⁿ < 52^{4n + 3}

n > ( 3log(52) ) / ( 2log(7) - 4log(52) )