005 Sample Final A, Question 7 - Revision history

Matt Lee at 03:22, 22 May 2015

2015-05-22T03:22:40Z

Matt Lee at 05:05, 11 May 2015

2015-05-11T05:05:17Z

Matt Lee: Created page with "''' Question ''' Solve the following equation, $2\log_5(x) = 3\log_5(4)$ {| class="mw-collapsible mw-collapsed" style = "text-align:left..."

2015-05-01T04:24:52Z

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..."

New page

''' Question ''' Solve the following equation,      <math> 2\log_5(x) = 3\log_5(4)</math>

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Final Answers
|-
|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>
|-
|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.
|-
|c) False. <math>y = x^2</math> does not have an inverse.
|-
|d) True. <math>cos^2(x) - cos(x) = 0</math> has multiple solutions.
|-
|e) True.
|-
|f) False.
|}

← Older revision		Revision as of 03:22, 22 May 2015
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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>
		+
		+	{\| 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>
		+	\|}

@@ Line 3: / Line 3: @@
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-! Final Answers
+! Step 1
 |-
-|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>
+| 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>
 |-
-|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.
+| By the definition of logarithm, we find that <math>x^2 = 4^3</math>
 |-
-|c) False. <math>y = x^2</math> does not have an inverse.
+| Taking the square root of both sides we get <math>x = 8</math>
 |-
-|d) True. <math>cos^2(x) - cos(x) = 0</math> has multiple solutions.
+| <math> x = 8</math>
 |}

005 Sample Final A, Question 7 - Revision history

Matt Lee at 03:22, 22 May 2015

Matt Lee at 05:05, 11 May 2015

Matt Lee: Created page with "''' Question ''' Solve the following equation, 2\log_5(x) = 3\log_5(4) {| class="mw-collapsible mw-collapsed" style = "text-align:left..."

Matt Lee: Created page with "''' Question ''' Solve the following equation, $2\log_5(x) = 3\log_5(4)$ {| class="mw-collapsible mw-collapsed" style = "text-align:left..."