MathAdmin: Created page with " Solve. $\log(x + 8) + \log(x - 1) = 1$ {| class="mw-collapsible mw-collapsed" style = "text-align:left;" !Foundations |- |1) How can we combine..."

2015-06-01T05:50:14Z

Created page with "<span class="exam"> Solve. <math>\log(x + 8) + \log(x - 1) = 1</math> {| class="mw-collapsible mw-collapsed" style = "text-align:left;" !Foundations |- |1) How can we combine..."

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<span class="exam"> Solve. <math>\log(x + 8) + \log(x - 1) = 1</math>
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!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:
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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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Solution:

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! 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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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! 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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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! 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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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! 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
<math> (0, \infty)</math>, -9 is removed as a potential answer. The answer is <math>x=2</math>.
|}

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Final Answer:
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| <math>x=2</math>
|}

[[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]

004 Sample Final A, Problem 15 - Revision history

MathAdmin: Created page with " Solve. \log(x + 8) + \log(x - 1) = 1 {| class="mw-collapsible mw-collapsed" style = "text-align:left;" !Foundations |- |1) How can we combine..."

MathAdmin: Created page with " Solve. $\log(x + 8) + \log(x - 1) = 1$ {| class="mw-collapsible mw-collapsed" style = "text-align:left;" !Foundations |- |1) How can we combine..."