Difference between revisions of "004 Sample Final A, Problem 15"

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!Foundations
 
!Foundations
 
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|1) How can we combine the two logs?
 
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|2) How do we remove logs from an equation?
 
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|Answer:
 
|Answer:
 
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|1) One of the rules of logarithms states that <math>\log(x)+\log(y)=\log(xy) </math>
 
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|2) The definition of the logarithm tells us that if <math>\log(x)=y</math>, then <math>10^y=x</math>.
 
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! Step 1:
 
! Step 1:
 
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|Using a rule of logarithms, the equation becomes <math>\log((x+8)(x-1))=1</math>.
 
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! Step 2:
 
! Step 2:
 
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|By the definition of the logarithm, <math>\log((x+8)(x-1))=1</math>
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|means <math>10=(x+8)(x-1)</math>
 
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! Step 3:
 
! Step 3:
 
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|Now, we can solve for <math>x</math>. We have <math>0=(x+8)(x-1)-10=x^2+7x-18=(x+9)(x-2)</math>.
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|So, there are two possible answers, which are <math>x=-9</math> or <math>x=2</math>.
 
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! Step 4:
 
! Step 4:
 
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|We have to make sure the answers make sense in the context of the problem. Since the domain of the log function is
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<math> (0, \infty)</math>, -9 is removed as a potential answer. The answer is <math>x=2</math>.
 
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! Final Answer:
 
! Final Answer:
 
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| <math>x=2</math>
 
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[[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]
 
[[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]

Latest revision as of 10:36, 29 April 2015

Solve.

Foundations
1) How can we combine the two logs?
2) How do we remove logs from an equation?
Answer:
1) One of the rules of logarithms states that
2) The definition of the logarithm tells us that if , then .

Solution:

Step 1:
Using a rule of logarithms, the equation becomes .
Step 2:
By the definition of the logarithm,
means
Step 3:
Now, we can solve for . We have .
So, there are two possible answers, which are or .
Step 4:
We have to make sure the answers make sense in the context of the problem. Since the domain of the log function is

, -9 is removed as a potential answer. The answer is .

Final Answer:

Return to Sample Exam

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