MathAdmin: 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;..."

2015-06-01T01:21:12Z

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,      <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>
|}

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 1
|-
| 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
|-
| 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
|-
| Taking the square root of both sides we get <math>x = 8</math>
|}

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Final Answer
|-
| <math> x = 8</math>
|}

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

005 Sample Final A, Question 7 - Revision history

MathAdmin: 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;..."

MathAdmin: 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;..."