27^y = 93^y ⇒ (3^3)^y = 93^y ⇒ 3^3y.3^y = 9 ⇒ 3^4y = 9 ⇒ 4y = log_39 = 2log_33 = 2 ⇒ y = 24 ⇒ y = 12 #160; ...

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Find y: 27y ...

Question

Find y:
$27^{y} = \frac{9}{3^{y}}$

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Solution

$27^{y} = \frac{9}{3^{y}}$

$\Rightarrow (3^{3})^{y} = \frac{9}{3^{y}}$

$\Rightarrow 3^{3 y} {.3}^{y} = 9$

$\Rightarrow 3^{4 y} = 9$

$\Rightarrow 4 y = l o g_{3} 9 = 2 l o g_{3} 3 = 2$

$\Rightarrow y = \frac{2}{4}$

$\Rightarrow y = \frac{1}{2}$

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