Solve for x, y and z :
$l o g_{4} z + l o g_{16} x + l o g_{16} y = 2$

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Solution

First equation can be written as
$l o g_{2} x + l o g_{2^{2}} y + l o g_{2^{2}} z = 2.$
or $l o g_{2} x + \frac{1}{2} l o g_{2} y + \frac{1}{2} l o g_{2} z = 2$
or $l o g_{2} \sqrt[x]{y z} = 2 o r \sqrt[x]{y z} = 2^{2} = 4$
or $x^{2}$ yz = 16.
similarly $y^{2}$ zx = 81
and $z^{2}$ xy = 256
The equations (1), (2) and (3) can now be easily solved. .
x = 2/3, y = 27/8, z = 32/3.
$l o g_{4} \frac{32}{3} + l o g_{16} \frac{2}{3} + l o g_{16} \frac{27}{8} = 2$

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