Logarithmic Function Review

Logarithm Equations

200

Solve:

log₁₀(x) = 2

x = 100

400

A number has a log base 10 of 3. What is the number?

hint: find what number you need x to be in order for the log equation to equal 3.

x = 1000

600

Find the exact answer of:

hint: convert to exponential first

log₇ (x + 5) = 3

The answer is:

x = 338

800

Solve for x:

Hint: use the product rule and convert

log₂(x) + log₂(x-2) = 3

The answer is:

x = 4

x = -2 DOES NOT WORK

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

Solve for x in the equation:

5^2x-1 = 125

1. Rewrite 125 with a base of 5: 5^2x-1 = 5³

2. Set the exponents equal to each other: 2x - 1 = 3

3. Solve for X: 2x = 4

4. Answer: x = 2

800

Solve this equation using logs: (hint - use a calculator and the change of base rule)

6^x = 50

Answer = 2.18

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