Logarithms

Rewrite

100

Rewrite log₃9=2 in exponential form

3²=9

200

Rewrite 4³=64 in logarithmic form

log₄64=3

300

Rewrite log₃(2x-3)=5 in exponential form

3⁵=2x-3

400

Rewrite log1000=3 in exponential form

10³=1000

500

Rewrite e⁴=3x in logarithmic form

ln3x=4

Expand/Condense

100

Expand log3x²

log3+2logx

200

Daily Double: Choose what to wager before turning to the question.

List the steps required for both expanding and condensing. 

300

Condense 3log₂x+log₂y

log₂x³y

400

Expand log₃(2x/y)

log₃2+log₃x-log₃y

500

Condense 2log₄3+4log₄z

log₄9z⁴

Graphs

100

What is the domain of log₃x?

(0,∞)

200

What is the range of log₂(x-3)?

(-∞,∞)

300

What is the vertical asymptote of log₃(x+1)?

x=-1

400

What is the domain AND range of log₂(x-3)+2?

Domain:(3,∞)

Range:(-∞,∞)

500

Graph log₂(x)+1

Evaluate in class

Solve

100

Use your calculator to solve log5. Round to the nearest thousandth.

0.699

200

Use your calculator to solve log₃5. Round to the nearest hundredth. 

1.46

300

Solve log₂(x+1)=6

2⁶-1=63

400

Solve 2^x-1=35. Round to the nearest hundredth.

6.13

500

Solve 2e^4x=36. Round to the nearest hundredth

0.72

Word problems

100

If money is invested into an account that compounds interest continuously an an annual rate of 4%, the amount in the account, A, is determined by the formula A=Pe^rt where P is the principal initially invested and t is the time in years. Write an equation to represent the time needed to increase a deposit of $500 to $1250.

1250=500e^0.04t

200

A scientist initially measures 8000 bacteria in a growth medium. It takes 3 hours for the bacteria to double. Assuming exponential growth, the formula P=C(2)^rt gives the number of bacteria in the growth medium, where r and C are constants and P is the number of bacteria t hours after the initial measurement. Write an equation that could be used to solve for r.

16000=8000(2)^3r

300

Daily double: Choose what to wager before viewing the question. This is a review topic.

Factor 2x²-7x-4

400

A business pays their employees a salary of S(t)=45,000+3,500ln(t), where t is an employee's years of experience. How much experience would you need to make $50,000?

5 years (4.173)

500

You deposit $1,200 into an account that pays 5% interest compounded continuously. How long will it take for your money to triple? Solve and round to the nearest hundredth. 

21.97 years