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

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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
asked Jan 27, 2015 in CALCULUS by anonymous

4 Answers

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(a)

Step 1:

The logarithmic value is .

Rewrite as .

Use product rule: .

substitute   and .

Solution:

.

answered Jan 27, 2015 by yamin_math Mentor
0 votes

(b)

Step 1:

The logarithmic value is  .

Use quotient rule: .

substitute the values of  and .

Solution:

.

answered Jan 27, 2015 by yamin_math Mentor
0 votes

 (c)

Step 1:

The logarithmic value is .

Rewrite as image.

Use power rule: .

 

Use product rule: .

substitute the values of  and .

Solution:

.

answered Jan 27, 2015 by yamin_math Mentor
0 votes

(d)

Step 1:

The logarithmic value is .

Rewrite as image.

Use power rule: .

substitute the value of  .

Solution:

.

answered Jan 27, 2015 by yamin_math Mentor

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