My Math Forum logarithmic expansion

 Algebra Pre-Algebra and Basic Algebra Math Forum

 April 13th, 2012, 05:11 AM #1 Member   Joined: Jan 2012 Posts: 47 Thanks: 0 logarithmic expansion Hi; I need to expand log4(x^2 + 9)/log4(x^2 - 6x + 8)^2/3. the 4 is tha base. 2/3log4(x^2 + 9) / 2/3log4(x^2 -6x + 8) 2/3log4x^2 + 9 - 2/3log4x^2 - 6x +8 This is where I not sure with the quadratic I guess you just expand it giving 2/2log4x^2 - 2/3log4(x - 2) + 2/3log4(x + 4) and thats it I think.
April 13th, 2012, 05:43 AM   #2
Math Team

Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
Thanks: 407

Re: loarithmic expansion

Hello, anthonye!

A strange problem . . . not much can be done with it.
Are you sure it says "expand"?

Quote:
 $\text{Expand: }\:\frac{\log_4(x^2\,+\,9)}{\log_4(x^2\,-\,6x\,+\,8)^{\frac{2}{3}}}$

$\text{The denominator expands:}
\;\;\;\log_4(x^2\,-\,6x\,+\,8)^{\frac{2}{3}} \;=\;\frac{2}{3}\,\!\log_4(x^2\,-\,6x\,+\,8)
\;\;\;\;\;=\;\frac{2}{3}\,\!\left[\log_4(x\,-\,2)(x\,-\,4)\right] \;=\;\frac{2}{3}\,\!\left[\log_4(x\,-\,2)\,+\,\log_4(x\,-\,4)\right]$

$\text{So we have: }\:\frac{\log_4(x^2\,+\,9)}{\frac{2}{3}\,\!\log_4( x\,-\,2)\,+\,\frac{2}{3}\,\!\log_4(x\,-\,4)}$

$\text{And that's it!}$

Edit: corrected the omission of the 2/3 power.

 April 13th, 2012, 05:49 AM #3 Member   Joined: Jan 2012 Posts: 47 Thanks: 0 Re: loarithmic expansion Surely the division becomes subtraction and you missed the 2/3 off.
April 13th, 2012, 09:35 AM   #4
Math Team

Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
Thanks: 407

Re: loarithmic expansion

Hello again, anthonye!

Quote:
 Surely the division becomes subtraction.[color=beige] . [/color][color=blue]No, it doesn't![/color]

$\frac{\log(a)}{\log(b)}\,\text{ does }not\text{ equal }\,\log(a)\,-\,\log(b)$

$\text{Think about it!}
\;\;\;\text{How can }\frac{A}{B}\text{ turn into }A\,-\,B\,?$

$\text{You are confusing it with: }\:\log\left(\frac{A}{B}\right) \;=\;\log(A)\,-\,\log(B)$

 April 13th, 2012, 10:40 AM #5 Member   Joined: Jan 2012 Posts: 47 Thanks: 0 Re: logarithmic expansion Ok thanks Soroban.

 Tags expansion, logarithmic

### 2 3log4

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post MATHEMATICIAN Number Theory 5 September 4th, 2013 07:53 AM apoorva Algebra 4 April 26th, 2013 11:20 PM myk Probability and Statistics 1 September 1st, 2010 07:50 PM davedave Algebra 1 November 19th, 2009 10:11 PM Sarge99 Algebra 4 October 15th, 2009 06:51 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top