LOGARITHM

Form Conversions

100

Rewrite 5³=125 in logarithmic form.

What is log₅125=3?

200

Rewrite log₂16=4 in exponential form.

What is 2⁴=16?

300

Evaluate log₄64.

What is 3? (Since 4³=64)

400

If log_bx=y, what is the exponential form?

What is b^y=x?

500

Evaluate log_bb^k.  

What is k?

Properties of Logs

100

The property that says log_b(MN)=log_bM+log_bN.

What is the Product Property?

200

Expand log₃(5x). 

What is log₃5+log₃x?

300

Condense 2logx−logy.

What is log(x²/y)?

400

 Condense: 2loga−(2logb+logc).

What is log(a²/b²c)?

500

Condense: log₂(x+3)+log₂(x−7).

What is log₂ (x-4x-21)?

Solving Log Equations

100

Solve for x: log₄x=2.

What is x = 16?

200

Solve for x: ln(x−1)=0.

What is x=2? (Since e⁰=1, so x−1=1)

300

Solve for x: log₂(x+5)=log₂9.

What is x = 4?

400

Solve for x: log₆x + log₆4=1. 

What is x=3/2 or x=1.5?

500

Solve for x: log₂(x)+log₂(x−7)=3. (Requires factoring and checking solutions!)

What is x = 8?

Log Base 'e' & Applications

100

The mathematical constant represented by the letter 'e'.

What is Euler's number (or the natural base)?

200

The name for the logarithm with base e, written as ln.

What is the Natural Logarithm?

300

The formula for continuously compounded interest, A, given principal P, rate r, and time t.

What is A=Pe^rt?

400

If a population is modeled by P(t)=50e^0.1t, what is the initial population?

What is 50?

500

If you invest $1000 at 5% interest compounded continuously, approximately how long will it take to double your money? (Use ln2≈0.70)

What is approximately 14 years?

Solving Exponential Equations

100

Solve for x: 3^x=81.

What is x = 4? 

200

Solve for x: 4^x+1=16.

What is x = 1?

300

Use logarithms to solve for x (round to nearest hundredth): 5^x=12.

What is x≈1.54?

400

Solve for x (round to nearest hundredth): 7^2x+1=20.

What is x≈0.76?

500

FINAL JEOPARDY! Solve for x: e^2x − 5 = 1. (Give the exact answer using ln).

What is x= ln(6)/2?