Logarithm Review

Logs :)

100

Logarithm property of a product? 

Logarithm of a product:

 = log_a(MN)+log_aM + log_aN

200

Logarithm property of a quotient?

Logarithm of a quotient:

= log_aM/N−log_aM - log_aN

300

Logarithm property of a power?

Logarithm of a power:

log_aM^p = p log_aM

400

Solve for x.

log_x100 = 2

Simplify your answer as much as possible.

The answer is x=10 

500

Write the expression as a single logarithm.

1/4log_cx + 5log_cz - log_cy

log_c (x^1/4 z⁵ / y)

Expanding Log Expressions

100

Evaluate each expression.

Reminder: When a logarithm is written "log" without an explicit base, it refers to the common logarithm, log₁₀

a) log₈ 1/8

b) log 1000

a) -1

b) 3

200

Use the properties of logarithms to expand log x/z⁴

Each logarithm should involve only one variable and should not have any exponents. Assume that all variables are positive. 

logx - 4logz

300

Use the properties of logarithms to expand the following expression. 

log rad(xy⁷ / z³)

Each logarithm should involve only one variable and should not have any radicals or exponents. You may assume that all variables are positive.

1/2logx + 7/2logy - 3/2logz

400

Use the properties of logarithms to expand log (z²x)

Each logarithm should involve only one variable and should not have any exponents. Assume that all variables are positive. 

2logz + logx

500

Use the properties of logarithms to expand the following expression.

log (y⁷ / rad(xz³))

Each logarithm should involve only one variable and should not have any radicals or exponents. You may assume that all variables are positive.

7logy - 1/2logx - 3/2logz

Converting Log to Exp

100

How can we rewrite this statement as a logarithmic equation?

b^e = n

log_b n = e

200

How can we rewrite this statement as an exponential equation?

log_a c = b

a^b = c

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

Rewrite each equation as requested.

(a) Rewrite as a logarithmic equation.

e⁵ = y

(b) Rewrite as an exponential equation.

lnx = 8

(a) lny = 5

(b) e⁸ = x

Random

100

What is the change of base formula for logarithms?

log_ab = log_cb / log_ca

200

Evaluate each expression.

(a) log₆ 6

(b) log₄ 1/64

(a) 1

(b) -3

300

Use the change of base formula to compute log₈3

Round your answer to the nearest thousandth. 

0.528

400

Find the domain of the function.

f(x) = log(x²-1)

Write your answer as an interval or union of intervals. 

Domain: (−∞,−1) ∪ (1,∞)

500

Use the change of base formula to compute log₈3

Round your answer to the nearest thousandth. 

0.528

SPTs :)

100

What is Alex's favorite candy?

Reese's

200

What is Mari's favorite Avatar character? 

Toph

300

What is Eric's dream pet?

Komodo Dragon

400

What is Mari's favorite song from SpongeBob?

This Grill is Not a Home 

OR

Gary Come Home

500

What are Halani's two favorite animals?

Bears and sharks