If $l o g_{3} y = x$ and $l o g_{2} z = x$ , find $72^{x}$ in terms of y and z

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Solution

We have,
$l o g_{3} y = x a n d l o g_{2} z = x$ ,

$\Rightarrow y = 3^{x} a n d z = 2^{x} \dots (i)$

Now,

$72^{x}$ $= (2^{3} \times 3^{2})^{x}$

$(2^{3})^{x} \times (3^{2})^{x}$

$= 2^{3 x} . 3^{2 x}$

$= (2^{x})^{3} (3^{x})^{2}$

$= (z)^{3} (y)^{2}$ [Using (i)]

$= y^{2} z^{3}$ .

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