Properties of Logarithms

Exponential Form

1

Evaluate log₂ 64

6

2

Evaluate log₄ 4

1

3

Evaluate log₅ 1

0

4

Evaluate log₄ (1/64)

-3

5

Evaluate log₂₅ 5

1/2

Expand

1

Expand  log (4n²)

log 4 + 2log n

2

Expand log₅ (x/15)

log₅(x) - log₅(15)

3

Expand log₂ xy^-1/2z

log₂x - 1/2 log₂y + log₂z

4

Expand log₇ (xy/z)

log₇ x + log₇ y - log₇ z

5

Expand log (xyz)^1/2

1/2logx + 1/2logy + 1/2logz

Condense/Evaluate

1

Condense  2log x + log 5

log (5x²)

2

Condense  log 8 - log x

log (8/x)

3

Evaluate log₂ 8 + log₂ 2

4

4

Evaluate log₄ 32 - log₄ 2

2

5

Evaluate   

2log₃ 3 + log₃ 9 - log₃ 3

3

Change of Base

1

Express log₅ 2 using common logs

log 2 / log 5

2

Evaluate log₁₂ 8 to the nearest hundredth

.84

3

Evaluate log₆ 15 to the nearest thousandth

1.511

4

Rewrite   log 7 / log 3 as a single log

log₃ 7

5

Evaluate   log_1/5 8 to the nearest thousandth

-1.292