assignment 38

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course mth 158

4 7/31

If your solution to stated problem does not match the given solution, you should self-critique per instructions at http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.

Your solution, attempt at solution:

If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

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(8) / log(3) * log(9) / log(8)

confidence rating #$&*: 3

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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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Self-critique (if necessary):

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Self-critique Rating: 3

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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) - 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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Self-critique (if necessary):

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Self-critique Rating: 3

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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(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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Self-critique (if necessary):

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Self-critique Rating: 3

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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)

=U^2 -V

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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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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Self-critique (if necessary):

I’m confused on why it ended up dividing u^2 by v? And it is a subtraction problem…why does it keep the log{base 3}?

@&
2^3 / 2^5 = 2^(3 - 5), but this isn't a subtraction problem.

2^3 - 2^5 is not 2^(-2), so the subtraction problem doesn't lead to a subtraction of exponents.

The rule for logs is

log(a) - log(b) = log(a / b).

The reasons go back to the rules for exponents, so it's no surprise that the subtraction on the left doesn't lead to a subtraction on the right.

*@

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Self-critique Rating: 1

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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:

Log(15)/log(1/2)

= -3.90

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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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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Self-critique (if necessary):

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Self-critique Rating: 3

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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:

(x + c) =e^y

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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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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Self-critique (if necessary):

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Self-critique Rating: 3

Self-critique (if necessary):

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Self-critique rating:

Self-critique (if necessary):

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Self-critique rating:

#*&!

assignment 38

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