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March 26th, 2012, 03:35 PM  #1 
Member Joined: Feb 2012 Posts: 94 Thanks: 0  Show the statement is true
How would you show this statement is true? I tried finding a common denominator for the left side then subtract, but I don't know what to do from there, I'm completely stumped, can anyone help me out please?

March 26th, 2012, 03:47 PM  #2 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: Show the statement is true
There's probably a slicker way (and I can think of who might know it...!), but I would use the change of base formula to rewrite the denominators as ln(a)/ln(2) ln(a)/[2ln(2)], and ln(a)/ln(2) Then do some algebra... 
March 26th, 2012, 04:19 PM  #3  
Member Joined: Feb 2012 Posts: 94 Thanks: 0  Re: Show the statement is true Quote:
 
March 26th, 2012, 04:21 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,209 Thanks: 517 Math Focus: Calculus/ODEs  Re: Show the statement is true
We are given: Use the identity to write: True. 
March 26th, 2012, 04:24 PM  #5 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: Show the statement is true
THERE we go!

March 26th, 2012, 04:28 PM  #6  
Member Joined: Feb 2012 Posts: 94 Thanks: 0  Re: Show the statement is true Quote:
How does the right side become a ?  
March 26th, 2012, 04:35 PM  #7 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,209 Thanks: 517 Math Focus: Calculus/ODEs  Re: Show the statement is true 
March 26th, 2012, 04:37 PM  #8  
Member Joined: Feb 2012 Posts: 94 Thanks: 0  Re: Show the statement is true Quote:
ahh I see, thank you very much! I really appreciate it!  
March 26th, 2012, 04:42 PM  #9  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 407  Re: Show the statement is true Hello, Lucida! I tried a "slicker" method and it turned out to be long and very involved. Quote:
[color=beige]. . [/color] Edit: Wow! . . . Lovely work, Mark! [color=beige] .[/color]  
March 26th, 2012, 05:08 PM  #10  
Member Joined: Feb 2012 Posts: 94 Thanks: 0  Re: Show the statement is true Quote:
Quote:
 

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