Question

Use the properties of logarithms to approximate the indicated logarithms, given that ln 2 ≈ 0.6931 and ln 3 ≈ 1.0986.

(a) ln 6           (b) ln 2/3             (c) ln 81             (d) ln √3

Answer 1

(a)

Step 1:

The logarithmic value is .

Rewrite as .

Use product rule: .

substitute   and .

Solution:

.

Answer 2

(b)

Step 1:

The logarithmic value is  .

Use quotient rule: .

substitute the values of  and .

Solution:

.

Answer 3

 (c)

Step 1:

The logarithmic value is .

Rewrite as .

Use power rule: .

 

Use product rule: .

substitute the values of  and .

Solution:

.

Answer 4

(d)

Step 1:

The logarithmic value is .

Rewrite as .

Use power rule: .

substitute the value of  .

Solution:

.