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

Revision as of 22:05, 10 May 2015

Question Solve the following equation, $2\log _{5}(x)=3\log _{5}(4)$

Step 1
Use the rules of logarithms to move the 2 and the 3 to exponents. So $\log _{5}(x^{2})=\log _{5}(4^{3})$

Step 2
By the definition of logarithm, we find that $x^{2}=4^{3}$

Step 3
Taking the square root of both sides we get $x=8$

Final Answer
$x=8$

@@ 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>
+|}
+{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+! Step 2
 |-
-|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>
+|}
+{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+! Step 3
 |-
-|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>
+|}
+{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+! Final Answer
 |-
-|d) True. <math>cos^2(x) - cos(x) = 0</math> has multiple solutions.
+| <math> x = 8</math>
-|-
-|e) True.
-|-
-|f) False.
 |}