Logarithm Review

Logs :)

100

What logarithm property is this:

log_a(MN) = log_aM + log_aN

Logarithm property of product

200

What logarithmic property is this:

log_a(M/N) = log_aM - log_aN

Logarithm quotient property

300

What Logarithm property is this:

log_aM^p = p log_aM

Logarithm power property

400

Solve for x.

log_x100 = 2

Simplify your answer as much as possible.

The answer is x=10 

500

Condense the expression as a single logarithm.

1/4log_cx + 5log_cz - log_cy

log_c 

((x^(1/4) z^5) / y)

Expanding Log Expressions

100

Evaluate each expression without using a calculator.

a) 8^{log₈ (1/8)}

b) log 1000

a) 1/8

b) 3

200

Expand 

log ((2xy^6)/(3z^4))

 

log x + 6 log y +log 2 - (log 3 + 4 log z)

300

Use the properties of logarithms to expand the following expression. 

log (root 2((xy^7) / z^3))

1/2 log x + 7/2 log y - 3/2 log z

400

Use the properties of logarithms to expand log (z²x)

2 log z + log x

500

Use the properties of logarithms to expand the following expression.

log (y^7 / root2(xz^3))

7 log y - (1/2 log x + 3/2 log z)

Solving Equations

100

Solve

log x + log 8 = 2

25/2

200

Solve

ln (4x+1) - ln 3 = 5

(3e^5 − 1) /4

300

Rewrite each equation as requested.

(a) Rewrite as an exponential equation.

log₃81 = 4

(b) Rewrite as a logarithmic equation.

8⁻¹ = 1/8

(a) 3⁴ = 81

(b) log₈1/8 = −1

400

Rewrite each equation as requested.

(a) Rewrite as an exponential equation.

ln5 = y

(b) Rewrite as a logarithmic equation.

e^x = 4

(a) e^y = 5

(b) ln4 = x

500

Solve

2^2x+1 - 38 = -6

x = 3

Random

100

John invests $1,289 in a retirement account with a fixed annual interest rate of 2.63% compounded continuously. How long will it take for the balance to reach $1,912.41? Round to the nearest whole number.

15 years 

200

Evaluate each expression.

(a) log₆ 6

(b) log₄ 1/64

(a) 1

(b) -3

300

Solve

log₅ (10+x) = 2

x=15

400

Find the domain and asymptote of the function.

f(x) = log(x-1)

 

Domain:  (1,∞)

Asymptote: x=1

500

In 2002 the population of schoolchildren in a city was 90,000. This population decreases at a rate of 5% each year. What will be the population of school children in year 2010?  Round to the nearest whole number.

How long will it take for the population to decrease to 45,000? Round to the nearest hundredth.

59,708

13.51 years

SPTs :)

100

What is the perfect bowling score?

300

200

What is the largest group on the food pyramid? 

Fruits and Vegetables

300

Which letter is representative of 50 in Roman numerals?

L

400

Where is the tallest building in the world located?

Dubai

500

What is C.S. Lewis’s first name?

Clive