Precalculus Homework

91

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1. -/2 points

Consider the following.

log2/7 X

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(a) Rewrite the logarithm as a ratio of common logarithm;.

(b) Rewrite the logarithm as a ratio of natural logarithm;.

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2. -/2 points

Consider the following.

log2 x

(a) Rewrite the logarithm as a ratio of common logarithm;.
(b) Rewrite the logarithm as a ratio of natural logarithm;.

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·IN, Fall 2013
3

LarATRMRP6 4.3.008.

LarATRMRP6 4.3.006.

119

129-4.3
~1113

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3. -/2 points

Consider the following.

log6,9 X

(a) Rewrite the logarithm as a ratio of corTTl”K>n logarithms.

(b) Rewrite the logarithm as a ratio of natural logarithms.

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LarATRMRP6 4.3.012.

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4. -/1 points
LarATRMRP6 4.3.014.

Evaluate the logarithm using the change-of-base fonrula. Round your result to three decimal

places.

log11( 4)

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5. -/1 points LarATRMRP6 4.3.016.

Evaluate the logarithm using the change-of-base fonrula. Round your result to three decimal
places.

log4(0.0i6)

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9121113 129-4.3
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6. -/1 points LarATRMRP6 4.3.022.

Rewrite the expression in terms of In 5 and In 6.

ln(5400)

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7. -/1 points LarATRMRP6 4.3.024.

Rewrite the expression in terms of In 4 and In 7.

In 2.
2

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8. -/10 points LarATRMRP6 4.3.039.MI.SA.

This question has several parts that must be completed sequentially. If you skip a part of the

question, you will not receive any points for the skipped part, and you will not be able to come

back to the skipped part.

Tutorial Exercise

Use the properties of logarithms to rewrite and Sirl’1Jiify the logarithrric expression.

log6(136 . 21613)

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129-4.3
9121113 ——————————————————————————————————————–

LarATRMRP6 4.3.040.
9. -/1 points

Use the properties of logarithms to rewrite and si~lify the logarithmic expression.

log 3(92 · 24 )

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10.-/1 points
LarATRMRP6 4.3.043.

Use the properties of logarithms to rewrite and si~lify the logarithmic expression.

ln(:7 )

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11.-/4 points

Use the properties of logarithms to verify the equation.

-In 24

= -{3 In 2 +In 3)

-In 24 = -In( 23 · )
=

-In 23 _

=
In 2-

= -{3 In 2 +In 3)

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LarATRMRP6 4.3.046.

419

~1/13 129-4.3

12.-/1 points LarATRMRP6 4.3.050.

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant

multiple of logarithms. (Assume all variables are positive.)

7 log10-

z

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13.-/1 points LarATRMRP6 4.3.052.

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant
multiple of logarithms. (Assume all variables are positive.)

1
logs3

z

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14.-/1 points LarATRMRP6 4.3.054.

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant
multiple of logarithms. (Assume all variables are positive.)

In( 8v/t)

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9121/13 129-4.3
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15.-/1 points LarATRMRP6 4.3.056.

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant

m.Jitiple of logarithms. (Assume all variables are positive.)

In .0y9
z8

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16.-/1 points LarATRMRP6 4.3.058.

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant
m.Jitiple of logarithms. (Assume all variables are positive.)

log4 xy7z4

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17.-/1 points LarATRMRP6 4.3.060.MI.

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant
m.Jitiple of logarithms. (Assume all variables are positive.)

( ….–) /.0 In v• yS

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9’21/13 129- 4.3
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18.-/6 points LarATRMRP6 4.3.060.MI.SA.

This question has several parts that must be completed sequentially. If you skip a part of the
question, you will not receive any points for the skipped part, and you will not be able to come
back to the skipped part.
Tutorial Exercise
Use the properties of logarithms to expand the expression as a sum, difference, and/or constant
multiple of logarithms. (Assume all variables are positive.)

( r;r;) In v/ y7

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19.-/1 points LarATRMRP6 4.3.061.

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant
multiple of logarithms. (Assume all variables are positive.)

In( x2 X~ 4 } X > 2

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20.-/1 points LarATRMRP6 4.3.062.

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant
multiple of logarithms. (Assume all variables are positive.)

Iu ( .r )
\”.r’1 + K

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SW21/13 129-4.3

21.-/1 points

Condense the expression to the logarithm of a single quantity.

In y +In z

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22.-/1 points

Condense the expression to the logarithm of a single quantity.

log2 9 – log2 t

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23.-/1 points

Condense the expression to the logarithm of a single quantity.

6 In x + ln(x + 1)

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24.-/1 points

Condense the expression into the logarithm of a single quantity.

ln(x) – 4 ln(x + 5)

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LarATRMRP6 4.3.070.

LarATRMRP6 4.3.072.

LarATRMRP6 4.3.076.

LarATRMRP6 4.3.078.

819