Difference between revisions of "005 Sample Final A, Question 7"

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(Created page with "''' Question ''' Solve the following equation,      <math> 2\log_5(x) = 3\log_5(4)</math> {| class="mw-collapsible mw-collapsed" style = "text-align:left...")
 
 
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''' Question ''' Solve the following equation, &nbsp;&nbsp;&nbsp;&nbsp; <math> 2\log_5(x) = 3\log_5(4)</math>
 
''' Question ''' Solve the following equation, &nbsp;&nbsp;&nbsp;&nbsp; <math> 2\log_5(x) = 3\log_5(4)</math>
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! Final Answers
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!Foundations
 
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|a) False. Nothing in the definition of a geometric sequence requires the common ratio to be always positive. For example, <math>a_n = (-a)^n</math>
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|1) What logarithm rule is relevant for dealing with the coefficients of the logarithms?
 
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|b) False. Linear systems only have a solution if the lines intersect. So y = x and y = x + 1 will never intersect because they are parallel.
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|2) How do we remove the logs?
 
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|c) False. <math>y = x^2</math> does not have an inverse.
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|Answer:
 
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|d) True. <math>cos^2(x) - cos(x) = 0</math> has multiple solutions.
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|1) One of the rules of logarithms says that <math> r\log(x) = \log(x^r)</math>
 
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|e) True.
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|2) The definition of logarithm tells us that if <math> \log_5(x) = y </math>, then <math> 5^y = x </math>
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! Step 1
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| Use the rules of logarithms to move the 2 and the 3 to exponents. So <math>\log_5(x^2) = \log_5(4^3)</math>
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! Step 2
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| By the definition of logarithm, we find that <math>x^2 = 4^3</math>
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! Step 3
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| Taking the square root of both sides we get <math>x = 8</math>
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! Final Answer
 
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|f) False.
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| <math> x = 8</math>
 
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Latest revision as of 20:22, 21 May 2015

Question Solve the following equation,     

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
2) The definition of logarithm tells us that if , then


Step 1
Use the rules of logarithms to move the 2 and the 3 to exponents. So
Step 2
By the definition of logarithm, we find that
Step 3
Taking the square root of both sides we get
Final Answer
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