Logarithmic Functions and Calculating Logarithms

row 1

100

ln (11)

2.398

200

log₉ (4)

0.631

300

log_13.5 (3)

0.42

400

log (1.75)

0.243

500

Write logarithmic expression as a single logarithm. 

A) log₄ 64 - log₄ 16

= log₄(64/16)          (logbM/N = logbM – logbN      Quotient Property)

= log₄ 4                  Simplify

= 1                         Simplify

row 2

100

log (3)

0.48

200

log₅ (3)

0.683

300

log₁₀ (50)

1.699

400

log_7.5 (10)

1.143

500

Write logarithmic expression as a single logarithm.

B) 6 log₅ x + log₅ y

= log₅ x⁶ + log₅ y                (logbMn = nlogbM     Power Property)

= log₅ (x⁶y)               (logbMN = logbM + logbN    Product Property)

row 3

100

ln (4)

1.3863

200

log₇ (2)

0.36

300

log₂ (0.40)

-1.322

400

log_0.5 (6)

-2.585

500

Expand each logarithm.

A) log₇ (t/u)

log₇ t - log₇ u

(logbM/N = logbM – logbN      Quotient Property)

row 4

100

ln (5.5)

1.705

200

log₅ (0.31)

-0.73

300

log_1.75 (0.5)

-1.24

400

log₁₀₀ (6)

0.39

500

Expand logarithm.

B) log(4p³)

= log 4 + log p³         (logbMN = logbM + logbN      Product Property)

= log 4 + 3 log p         (logbMn = nlogbM        Power Property)

row 5

100

ln (9)

2.2

200

log₃ (32.1)

3.1575

300

log₁₀₀ (25.75)

0.71

400

log _9.01 (4)

0.631

500

Use the Change of Base Formula to evaluate log₆12.

log₆12=(log 12) / (log 6)

≈1.387