Difference between revisions of "005 Sample Final A, Question 7"
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''' Question ''' Solve the following equation, <math> 2\log_5(x) = 3\log_5(4)</math> | ''' Question ''' Solve the following equation, <math> 2\log_5(x) = 3\log_5(4)</math> | ||
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| + | {| class="mw-collapsible mw-collapsed" style = "text-align:left;" | ||
| + | !Foundations | ||
| + | |- | ||
| + | |1) What logarithm rule is relevant for dealing with the coefficients of the logarithms? | ||
| + | |- | ||
| + | |2) How do we remove the logs? | ||
| + | |- | ||
| + | |Answer: | ||
| + | |- | ||
| + | |1) One of the rules of logarithms says that <math> r\log(x) = \log(x^r)</math> | ||
| + | |- | ||
| + | |2) The definition of logarithm tells us that if <math> \log_5(x) = y </math>, then <math> 5^y = x </math> | ||
| + | |} | ||
Latest revision as of 20:22, 21 May 2015
Question Solve the following equation, 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 2\log_5(x) = 3\log_5(4)}
| Foundations |
|---|
| 1) What logarithm rule is relevant for dealing with the coefficients of the logarithms? |
| 2) How do we remove the logs? |
| Answer: |
| 1) One of the rules of logarithms says that 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 r\log(x) = \log(x^r)} |
| 2) The definition of 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_5(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 5^y = x } |
| Step 1 |
|---|
| Use the rules of logarithms to move the 2 and the 3 to exponents. So 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_5(x^2) = \log_5(4^3)} |
| Step 2 |
|---|
| By the definition of logarithm, we find that 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 = 4^3} |
| Step 3 |
|---|
| Taking the square root of both sides we get 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 = 8} |
| 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 = 8} |