Question

2^x=3^y=12 then value of (x+2y)/xy

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

1

Step-by-step explanation:

Given :

$2^x = 3^y = 12$

To find the value of :

$\frac{x + 2y}{xy}$

Solution :

⇒ $log_{2}12 = x$

⇒ $log_2(2 \times 2 \times 3) = log_{2}(2^2 \times 3) = log_{2}2^2 + log_23 = 2log_22 + log_23= 2 + log_23$

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⇒ $log_{3}12 = y$

⇒ $log_{3}12 = log_3(3 \times 2 \times 2) = log_33+log_3(2 \times 2)= 1 + log_34 = 1 + \frac{log_2{4}}{log_2{3}} = 1+\frac{2}{log_2{3}} = \frac{2 + log_23}{log_23}$

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⇒ $\frac{x + 2y}{xy} = \frac{x}{xy} + \frac{2y}{xy} = \frac{1}{y} + \frac{2}{x}$

⇒ $\frac{1}{\frac{2+log_23}{2}} + \frac{1}{\frac{2+log_23}{log_23}}=\frac{2}{2+log_23} + \frac{log_23}{2+log_23} = \frac{2 + log_23}{2+log_23} = 1$