Assignment 38

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course mth 158

038. * 38

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Question: * 6.5.24 / 6.5.18 / 7th edition 5.5.18. Exact value of log{base 3}{(8) * log{base 8}(9).

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Your solution:

log{base 3}(8) * log{base 8}(9)

log 8 / log 3 * log 9 / log 8

log 9 / log 3 = log{base 3}(9)

log{base 3}(8) * log{base 8}(9) = 2

confidence rating #$&*:2

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Given Solution:

* * log{base 3}(8) * log{base 8}(9) = log 8 / log 3 * log 9 / log 8 = log 9 / log 3 = log{base 3}(9).

log{base 3}(9) is the power to which 3 must be raised to get 9, and is therefore equal to 2.

Thus log{base 3}(8) * log{base 8}(9) = 2.

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Question: * 6.5.30 / 6.5.24 / 7th edition 5.5.24. ln(2) = a, ln(3) = b. What is ln(2/3) in terms of a and b?

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Your solution:

Ln(2/3)=ln(2)-ln(3)=a-b

confidence rating #$&*:3

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Given Solution:

* * ln(2/3) = ln(2) - ln(3) = a - b.

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Question: * 6.5.32 / 6.5.26 / 7th edition 5.5.26. ln(0.5) in terms of a and b.

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Your solution:

ln(.5) = ln(1/2) = ln(1) - ln(2) = 0 - a = -a

confidence rating #$&*:3

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Given Solution:

* * Since ln(2) = a, and since ln(1) = 0, we have

ln(.5) = ln(1/2) = ln(1) - ln(2) = 0 - a = -a.

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Question: * Extra problem / 6.5.52 / 7th edition 5.5.52. log{base 3}(u^2) - log{base 3}(v) as a single log.

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Your solution:

log{base 3}(u^2) - log{base 3}(v) = log{base 3}(u^2 / v)

confidence rating #$&*: 2

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Given Solution:

* * log{base 3}(u^2) - log{base 3}(v) = log{base 3}(u^2 / v).

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Question: * Extra Problem / 6.5.58 / 7th edition 5.5.68. Using a calculator express log{base1 / 2}(15)

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Your solution:

og{base 1/2}(15) = log(15) / log(1/2) = 1.176091259 / )-0.3010299956) = -3.906890595

confidence rating #$&*: 2

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Given Solution:

* * We get log{base 1/2}(15) = log(15) / log(1/2) = 1.176091259 / )-0.3010299956) = -3.906890595.

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Question: * 6.5.88 / 6.5.82 / 7th edition 5.5.80. Express y as a function of x if ln y = ln(x + C).

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Your solution:

a = ln(b)

e^a = b

y = ln(x+c)

(x+c) = e^y

confidence rating #$&*: 1

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Given Solution:

* * a = ln(b) means e^a = b, so y = ln(x+c) is translated to exponential form as

(x+c) = e^y.

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