Please help me!

Please post a solution to the given problem. Any help would be appreciated. Thanks!

If $2^{x}$ = $4^{y}$ = $8^{z}$ and $xyz = 288$ , find the values of $x$, $y$ and $z$.

#Algebra #Exponents

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Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
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`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

We have $2^{x} = 2^{2y} = 2^{3z} \Longrightarrow x = 2y = 3z \Longrightarrow y = \dfrac{x}{2}, z = \dfrac{x}{3}.$

Thus $xyz = x*\dfrac{x}{2} * \dfrac{x}{3} = \dfrac{x^{3}}{6} = 288 \Longrightarrow x^{3} = 1728 \Longrightarrow x = 12, y = 6, z = 4.$

Brian Charlesworth - 6 years, 1 month ago

@Brian Charlesworth Sir you are quick enough to post the solution. As I am not good at LaTex , I could not post the solution quick. Thank you for posting the solution.

Manish Dash - 6 years, 1 month ago

You had the correct answer first. 3 minutes after the question was posted; that's fast! :)

Brian Charlesworth - 6 years, 1 month ago

@Brian Charlesworth – Thank you Sir. I am greatly obliged to get your compliment.

Manish Dash - 6 years, 1 month ago

I convey my heartfelt thanks to you respected Sir! @Brian Charlesworth

Swapnil Das - 6 years, 1 month ago

You're welcome, Swapnil. :)

Brian Charlesworth - 6 years, 1 month ago

Is the answer like this: x = 12, y=6, z=4

Manish Dash - 6 years, 1 month ago

Yes! Thank U! Please post the solution.

Swapnil Das - 6 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$