Quiz 7 Review

Conversion

100

Convert to logarithmic form 

4^x = 17 

Log₄(17) = x 

200

Convert to exponential form 

log₃(x) = 31

3³¹ = x

300

Convert to logarithmic form. Make sure your answer in simplest form 

10^x = 30,000

log(30,000) = x 

NOT

log₁₀(30,000) = x

400

Convert to logarithmic form 

e¹² = x

ln(x) = 12 

500

Convert to logarithmic form. Write your answer is simplest form. 

10^2x = y 

log₁₀₀y = x

Laws of Logarithms 1

100

Combine into a single logarithm 

log(4) + log(5)

log(20) 

200

Combine into a single logarithm

log(12) - log(3) 

log(4) 

300

Simplify 

2log₄(3)

log₄(9)

400

Simplify completely 

3log₂₁₆(6)

1

500

Simplify completely 

log₃(2x - 5y) 

when x = 3 and y = 1

0

Laws of Logarithms 2

100

Combine into a single logarithm 

log₂(10) + log₂(9) - log₂(15) 

log₂(6) 

200

Combine into a single logarithm 

log(8) / log(9)

log₉(8)

300

Convert into a single logarithm 

log3/log4 + log5/log4

log₄15

400

convert into a single logarithm 

(log(3) + log(15) - log(9))/(log(4) + log(2) 

log₈(5)

500

Convert into a single logarithm

(ln(14) + 3ln(2) - ln(4))/(ln(36) - 2ln(3))

log₄28

Exponential Equations

100

Find the value of x. Round your answer to two decimal places. 

4^x = 215

The value of x is about 3.87 

200

Find the value of x. Round your answer to two decimal places

6^2x = 18

The value of x is about 0.81

300

Find the value of x. Round your answer to two decimal places. 

3^{x + 5} = 2^3x

The value of x is about 5.6 

400

Solve the equation

2^{2x + 1} = 3^3x

Round your answer to two decimal places. 

The value of x is about 0.36

500

Solve the equation 

6^{3x - 2} = 8^{2x + 1}

Round your answer to two decimal places. 

The value of x is about 4.66

Radians

100

Convert 45 degrees to radians. 

pi/4

200

Convert into degrees

8pi 

1440 degrees

300

Convert into degrees

pi/15

12 Degrees 

400

Convert 105 degrees into radians. Do not round. 

(7pi)/12

500

Convert 750 degrees into radians. Do not round. 

(25pi)/6