MathAdmin at 17:51, 2 June 2015

2015-06-02T17:51:45Z

MathAdmin: Created page with "''' Question ''' Solve the following equation, $3^{2x} + 3^x -2 = 0$ {| class="mw-collapsible mw-collapsed" style = "text-align:left;"..."

2015-06-01T01:22:02Z

Created page with "''' Question ''' Solve the following equation, <math> 3^{2x} + 3^x -2 = 0 </math> {| class="mw-collapsible mw-collapsed" style = "text-align:left;"..."

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''' Question ''' Solve the following equation,      <math> 3^{2x} + 3^x -2 = 0 </math>

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!Foundations
|-
|1) What substitution can we make to simplify the problem?
|-
|Answer:
|-
|1) Substitute <math>y = 3^x</math> to change the original equation into <math>y^2 + y - 2 = 0</math>
|}

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 1:
|-
| Start by rewriting <math>3^{2x} = \left(3^x\right)^2</math> and make the substitution <math>y = 3^x</math>
|}

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 2:
|-
| After substitution we get <math>y^2 + y - 2 = (y + 2)(y - 1)</math>
|}

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 3:
|-
| Now we have to find the zeros of <math>3^x + 2 = 0</math> and <math>3^x - 1 = 0</math>. We do this by first isolating <math>3^x</math> in both equations.
|-
|So <math>3^x = -2</math> and <math>3^x = 1</math>
|}

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 4:
|-
| We observe that <math>3^x = -2</math> has no solutions. We can solve <math>3^x = 1</math> by taking <math>log_3</math> of both sides.
|-
|This gives<math>\log_3\left(3^x\right) = x = \log_3(1) = 0</math>
|}

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Final Answer:
|-
| x = 0
|}

[[005 Sample Final A|'''<u>Return to Sample Exam</u>''']]

@@ Line 38: / Line 38: @@
 | We observe that <math>3^x = -2</math> has no solutions. We can solve <math>3^x = 1</math> by taking <math>log_3</math> of both sides.
 |-
-|This gives<math>\log_3\left(3^x\right) = x = \log_3(1) = 0</math>
+|This gives <math>\log_3\left(3^x\right) = x = \log_3(1) = 0</math>
 |}

005 Sample Final A, Question 8 - Revision history

MathAdmin at 17:51, 2 June 2015

MathAdmin: Created page with "''' Question ''' Solve the following equation, 3^{2x} + 3^x -2 = 0 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"..."

MathAdmin: Created page with "''' Question ''' Solve the following equation, $3^{2x} + 3^x -2 = 0$ {| class="mw-collapsible mw-collapsed" style = "text-align:left;"..."