Logarithmic Function Review

Logarithm Equations

200

If I have a log₁₀1000 = X

What is x?

Answer:

x = 3

400

Solve for X:

log₁₀(x) = 2

Answer:

x = 100

600

Solve for X:

log₂(x+2) + log₂(3) = log₂(27)

hint: use the product rule to find what x needs to be to equal log₂(27)

The answer is:

x = 7

800

Solve this log equation:

log₄(2x+6) - log₄(x-1) = 1

Hint: Use the quotient property, and combine the two logs into one

Answer:

x = 5

Exponential Equations

200

Solve:

2^x = 8

x = 3

400

If a value triples every week. Starting at 1, what is it after 3 weeks?

The answer is 27

600

Find the exact answer of:

log₇ (x + 5) = 3

hint: convert to exponential first

The answer is:

x = 338

800

Solve for x in the equation:

8^x+2 = 16^x+1

Hint: identify the common base first

Answer:

x = 2

Logarithm Rules

200

Which rule turns multiplication inside a log into addition?

The Product Rule

400

Which rule turns division inside a log into subtraction? 

The Quotient Rule

600

Which rule moves an exponent to the front of a log?

The Power Rule

800

Which rule rewrites a log using a different base?

The Change of Base rule

Logarithmic Graph Function

200

Identify what is the vertical asymptote of: 

y = log(x)

x = 0

400

If a log graph shifts right 4 units, how does the equation change?

(x - 4)

600

What is the vertical asymptote of:

y = log (x - 2)

x = 2

800

What transformation does this equation represent?

y = - log (x - 1)

To The Right 1 unit, Reflection Over X-Axis