Show how to simplify the following number by hand:
4^{log5/44}
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5^{log5/45}
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 20101102 19:15:01 