Please help me out of this mathematics problem.

The greatest integer x which satisfy $3^{20} > 32^{x}$ .

#HelpMe! #MathProblem #Math

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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}`	$\boxed{123}$

Comments

We have to find the greatest integer which satisfies $3^{20}$ $> 32^x$

$\Rightarrow$ $3^{20}$ $> 2^{5x}$

$\Rightarrow$ $\sqrt[5]{3^{20}}$ $> \sqrt[5]{2^{5x}}$

$\Rightarrow$ $3^4$ $> 2^x$

$\Rightarrow$ $81$ $> 2^x$

$81$ $> 64$

$\Rightarrow$ $x = 6$

Anoopam Mishra - 7 years, 12 months ago

_Hint: _ $32 = 2^5$ .

Calvin Lin Staff - 7 years, 12 months ago

do reeshab u read at fiitjee cuz this problem was given there

superman son - 7 years, 12 months ago

hey! are you in fiitjee? if yes please tell the centre. I am in fiitjee south delhi.

Anoopam Mishra - 7 years, 12 months ago

step 1 :: 20 log3 > x log 32. step 2 :: 20*0.477 > x 1.505. step 3 :: 6.33 > x. therefore x = 6.

Satish Kumar - 7 years, 12 months ago

You all are awesome, Brilliant.org is so cool :D

Reeshabh Ranjan - 7 years, 5 months 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}`	$\boxed{123}$