Logs Test Review

Simplifying Log Expressions

100

Write as a Single Log: Log₃(x) + Log₃(4)

Log₃(4x)

200

Write as a Single Log: Log₄(a) - Log₄(b) + Log₄(c)

Log₄(ac/b) 

300

Write as a single log, then evaluate: 

Log₄(80) - Log₄(5)

Log₄(16) = 2 

400

Simplify by hand: Log₃(54) - Log₃(2) + 2Log₃(3)

5

500

Write as a Single Log: 3Log₂(3) - Log₂(9) + Log₂(5)

Log₂(15)

Solving Log Equations

100

Log₂(x) = Log₂(6)

x = 6 

200

Log₂(2) + Log₉(x) = 1 

x = 1

300

3 + Log₄(2x - 3) + 2 = 5 

x = 2

400

Log₃(x + 1) + Log₃(4) = Log₃(8)

x = 1

500

Log₂(x) + Log₂(x + 2) = 3 

x = 2 

Solving Exponential Equations

100

2^x = 32

x = 5

200

3²ⁿ + 4 = 18

(Round to nearest thousandth) 

n = 1.201

300

4^{2w - 7} - 5 = 11

w = 4.5 

400

3e^{x - 1} - 8 = 20

(Round to the nearest hundredth)

x = 3.23

500

5^p(5^{2p + 1}) = 125

p = 2/3

Word Problems

100

If my $1 investment grows 50% each day, how long will it take my investment to grow to $50? (Round to nearest tenth)

9.6 days 

200

If a $10000 car depreciates 5% per year, how long will it take for the car to be worth $8000? (Round to nearest tenth)

4.4 years 

300

A population of 4 bacteria doubles every hour. How long will it take the bacteria to grow to 4096? 

10 hours 

400

A population of deer starts at 50 and grows 8% per year. How many months will it take the population to grow to 70? (Round to the nearest whole number) 

52 months

500

A population of 2 bacteria triples every 6 hours. How long will it take for the bacteria to reach a population of 200? (Round to the nearest whole) 

25 hours 

Log to Exponential, Exponential to Log

100

Rewrite the following in exponential form: Log₂(x) = 3

2³ = x 

or x = 2³

200

Rewrite the following in Log Form: 1.04^t = 5

t = Log_1.04(5)

300

Rewrite the following in Log Form: 3^{n + 2} = 18 

Log₃(18) = n + 2 

400

Write in Exponential Form AND solve for x: 

Log₂(x + 7) = 3

2³ = x + 7 

x = 1

500

Simplify the expression as much as possible by hand: 

Log₂(8) + Log₃(3) - Log₄(1) 

3 + 1 - 0 = 4