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March 26th, 2012, 02:35 PM   #1
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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?
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March 26th, 2012, 02:47 PM   #2
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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...
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March 26th, 2012, 03:19 PM   #3
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Re: Show the statement is true

Quote:
Originally Posted by The Chaz
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...
I don't follow, can you please explain it a bit simpler =X
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March 26th, 2012, 03:21 PM   #4
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Re: Show the statement is true

We are given:



Use the identity to write:







True.
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March 26th, 2012, 03:24 PM   #5
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Re: Show the statement is true

THERE we go!
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March 26th, 2012, 03:28 PM   #6
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Re: Show the statement is true

Quote:
Originally Posted by MarkFL
We are given:



Use the identity to write:







True.

How does the right side become a -?
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March 26th, 2012, 03:35 PM   #7
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Re: Show the statement is true

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March 26th, 2012, 03:37 PM   #8
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Re: Show the statement is true

Quote:
Originally Posted by MarkFL

ahh I see, thank you very much! I really appreciate it!
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March 26th, 2012, 03:42 PM   #9
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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]




[color=beige]. . [/color]

















Edit: Wow! . . . Lovely work, Mark!
[color=beige] .[/color]
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March 26th, 2012, 04:08 PM   #10
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Re: Show the statement is true

Quote:
Originally Posted by soroban
Hello, Lucida!

I tried a "slicker" method and it turned out to be long and very involved.


Quote:


[color=beige]. . [/color]




[color=beige]. . [/color]

Mark's method is a lot shorter and easier to understand, but thank you anyways!

Quote:













Edit: Wow! . . . Lovely work, Mark!
[color=beige] .[/color]
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