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Lost Logarithm (Posted on 2010-11-02) Difficulty: 3 of 5
Show how to simplify the following number by hand:

4log5/44 5log5/45

No Solution Yet Submitted by Jer    
Rating: 3.0000 (2 votes)

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Full Solution | Comment 2 of 3 |

Call the exponent in the numerator X, and that in the denominator Y.  Focusing on Y, Note that 5 = (5/4) * 4, so Y becomes log (base 5/4) (4 * 5/4), which can be simplified to X + 1.

Rewrite the problem as (4^X)/(5^(X+1)), and rewrite again to
4^X/5^X * (1/5) = (4/5)^X * (1/5) = (5/4)^(-X) * (1/5).  Substituting X back into the equation:

(5/4)^(-log(base(5/4)) 4 = 1/4, so the answer is 1/4 * 1/5 = 1/20


  Posted by Kenny M on 2010-11-02 19:15:01
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