Difference between revisions of "004 Sample Final A, Problem 19"
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!Foundations | !Foundations | ||
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| − | | | + | |How do we remove the log? |
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|Answer: | |Answer: | ||
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| − | | | + | |The definition of the logarithm tells us that if <math>\log_6(x)=y</math>, then <math>6^y=x</math>. |
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! Step 1: | ! Step 1: | ||
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| − | | | + | |By the definition of the logarithm, <math>\log_6 \frac{1}{36} = x</math> means <math>6^x=\frac{1}{36}</math>. |
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! Step 2: | ! Step 2: | ||
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| − | | | + | |Now, we can solve for <math>x</math>. Since <math>6^x=\frac{1}{36}</math>, |
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| − | | | + | |we must have <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>''']] | ||
Revision as of 10:12, 29 April 2015
Solve for x: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \log_6 \frac{1}{36} = x}
| Foundations |
|---|
| How do we remove the log? |
| Answer: |
| The definition of the logarithm tells us that if Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \log_6(x)=y} , then Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 6^y=x} . |
Solution:
| Step 1: |
|---|
| By the definition of the logarithm, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \log_6 \frac{1}{36} = x} means Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 6^x=\frac{1}{36}} . |
| Step 2: |
|---|
| Now, we can solve for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} . Since Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 6^x=\frac{1}{36}} , |
| we must have Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x=-2} . |
| Final Answer: |
|---|
| Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x=-2} |