Log Review Jeopardy

Converting Logs

100

Convert log₂8 = x into exponential form.

2^x = 8

200

Convert logx = 2 into exponential form.

10² = x

300

Convert lnx = 2 into exponential form.

e² = x

400

Convert e^x = e² into logarithmic form.

lne² = x

500

Convert logx = -0.523 into exponential form, then solve for x.

10^-0.523 = x

x = .299

Product Rule

100

Expand ln2xy using the product rule.

ln2 + lnx + lny

200

Expand log28 using the product rule.

log2 + log14 

300

Condense log3 + logx + logy + logz using the product rule.

log3xyz

400

Expand log₃5y using the product rule.

log₃5 + log₃y

500

Condense log₂9 + log₂5 using the product rule.

log₂45

Power Rule

100

Using the power rule, alter logx²

2logx

200

Using the power rule, alter log₂x⁴

4log₂x

300

Using the power rule, alter both

- 54log₃x

- log2^x

log₃x⁵⁴

xlog2

400

Using the power rule, alter all three

- 2log_x4

- log34⁵⁶

- 1000logx

log_x4²

56log34

logx¹⁰⁰⁰

500

Using the power rule and product rule, alter expand log(ab)²

2loga + 2logb

Quotient Rule

100

Condense logx - logy - logz using the quotient rule

log(x/y/z) or log(x/yz)

200

Expand log3 using the quotient rule

log6 - log2

300

Condense ln(u) - ln(v) using the quotient rule

ln(u/v)

400

Fully expand ln(12x/y) using the quotient rule

ln(12) + ln(x) - ln(y)

500

Expand log₁₄(14/x) using the quotient rule

log₁₄14 - log₁₄x

Random

100

Correctly identify this rule (product, quotient, change of base, power)

log_bx = logx/logb

Change of base formula

200

How tall is the Empire State Building? (within 200 feet gets point)

1,250 feet

300

Correctly identify this rule (product, quotient, change of base, power)

log_axⁿ = nlog_ax

Power rule

400

Correctl identify this rule (product, quotient, change of base, power)

log_a(x/y) = log_ax + log_ay

Product Rule

500

Correctly identify this rule (product, quotient, change of base, power)

log_a(x/y) = log_a(x) - log_a(y)

Quotient rule