Properties of logarithms

Quotient property of logarithms

What does it equal?

Power property of logarithms

Argument’s exponent brought to the front to be multiplied by everything else

Product property of logarithms

Simplify

What are the 3 rules/properties applied to get the solution. Solve

For expansion and compression which order of properties do you use for each?

For expansion

1. Quotient property of logarithms

2. Product property of logarithms

3. Power property of logarithms

Inverse order for each

For compression

1. Power property of logarithms

2. Product property of logarithms

3. Quotient property of logarithms

Expansion:

Solve and state each property, but only look at the answers 1 line at a time as you answer. Solve one property at a time while checking answers.

1. Quotient property of logarithms

2. Product property of logarithms

3. Power property of logarithms

Expansion:

Solve and state each property, but only look at the answers 1 line at a time as you answer. Solve one property at a time while checking answers.

1. Quotient property of logarithms

2. Product property of logarithms

3. Power property of logarithms

Compression:

state each property used to compress into a single logarithm, but only look at the answers 1 line at a time as you answer. Compress one property at a time while checking answers.

1. Power property of logarithms

2. Product property of logarithms

3. Quotient property of logarithms

4. (Optional) n-th root rule to rid of fractional exponent

Compression:

state each property used to compress into a single logarithm, but only look at the answers 1 line at a time as you answer. Compress one property at a time while checking answers.

1. Power property of logarithms

2. Product property of logarithms

3. Quotient property

4. Simplify fraction and cancel out

Change of base formula

Can be log with any base, as long as the base in the numerator and denominator match. Doesn’t need to be common log, the bases simply must match for both sides of the fraction.

Solve to the point to where you’d need a calculator to finish solving