Logarithims

bettyh

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Joined
Mar 20, 2011
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Find the rational ordered pair (x,y) for which....4 to the power of log base 16 of 27 = 3^y times 2^x
 
This is wonderful problem. i don't want to spoil it for you.

\(\displaystyle log_{16}(27) = \frac{log(27)}{log(16)} = \frac{log(3^{3})}{log(4^{2})} = \frac{log(3^{3})}{2\cdot log(4)} = \frac{(1/2)\cdot log(3^{3})}{log(4)} = \frac{log(3^{3/2})}{log(4)} = log_{4}(3^{3/2})\)

\(\displaystyle 4^{log_{16}(27)} = 4^{log_{4}(3^{3/2})} = 3^{3/2}\)

Now what?
 
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