assignment 65

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course Mth 158

12/14 2

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Question: *  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:

y=log(base b)(x) is b^y=x aaaand you can solve for y by saying ln(b^y)=ln(x) which becomes y*ln(b)=ln(x) and divide both sides by ln(b). so applying this question to the formula etc- you eventually get

[ln(8)/ln(3)]*[ln(9)/ln(8)]=2

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):ok

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Self-critique Rating:ok

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Question: *  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:

log(base a)(m/n) = log(base a)M- log(base a)n

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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Self-critique (if necessary):ok

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Self-critique Rating:ok

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Question: *  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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Self-critique (if necessary):

ok

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Self-critique Rating:ok

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Question: *  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:

ln(a)-ln(b)=ln(a/b)

so ln(a)=log{base 3}(u^2) and ln(b)=log{base 3}(v) you have

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

confidence rating #$&*: 3

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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):ok

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Self-critique Rating:ok

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

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Your solution:

1/2^y=15 is log{base1 / 2}(15)

log(1/2^y)=log(15)

y*log(1/2)=log(15)

y=log(15)/log(1/2)

y= -3.906890596

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):ok

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Self-critique Rating:ok

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Question: *  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:

y=log(base a)(x) means x=a^y but x(ln(b) means e^x=b

ln(y) = ln(x + C) means (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):

ok

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Self-critique (if necessary):

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Self-critique rating:

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