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March 13th, 2016, 01:50 PM  #1 
Senior Member Joined: Jan 2012 Posts: 725 Thanks: 7  Find log x in terms of a and b.
If $\log(x^3 y^2)=a$ and $\log (\frac{y}{x})=b$ find log x in terms of a and b. How do I go about this?
Last edited by skipjack; March 16th, 2016 at 02:03 PM. 
March 13th, 2016, 02:00 PM  #2  
Math Team Joined: Jul 2011 From: Texas Posts: 2,838 Thanks: 1481  Quote:
$3\log{x} + 2\log{y} = a$ $\log{y}\log{x} = b$ multiply each term of the second equation by 2 and add to the first equation ... $3\log{x} + 2\log{y} = a$ $2\log{y}+2\log{x} = 2b$  $5\log{x} = a2b$ $\log{x} = \dfrac{a2b}{5}$  
March 16th, 2016, 01:11 PM  #3 
Senior Member Joined: Jan 2012 Posts: 725 Thanks: 7 
But without adding the two equations to eliminate logy, how else can this be done?

March 16th, 2016, 01:31 PM  #4  
Math Team Joined: Jul 2011 From: Texas Posts: 2,838 Thanks: 1481  Quote:
substitute $(b+\log{x})$ in for $\log{y}$ in the first equation ... $3\log{x}+2(b+\log{x}) = a$ $3\log{x} + 2\log{x} + 2b = a$ $5\log{x} = a2b$ $\log{x} = \dfrac{a2b}{5}$  
March 16th, 2016, 08:52 PM  #5 
Senior Member Joined: Jan 2012 Posts: 725 Thanks: 7 
Alright! Thank you. Apart from elimination and substitution method, any other method?

March 17th, 2016, 05:06 AM  #6 
Math Team Joined: Jul 2011 From: Texas Posts: 2,838 Thanks: 1481 
What method are you looking for ... ?

March 17th, 2016, 07:46 AM  #7 
Senior Member Joined: Jan 2012 Posts: 725 Thanks: 7 
No other method.

March 17th, 2016, 09:48 AM  #8 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry  

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