Excel in math, science, and engineering

New user? Sign up

Existing user? Sign in

The greatest integer x which satisfy \(3^{20} > 32^{x}\).

Note by Reeshabh Ranjan 4 years, 2 months ago

Sort by:

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 · 4 years, 2 months ago

Log in to reply

_Hint: _ \( 32 = 2^5 \). – Calvin Lin Staff · 4 years, 2 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 · 4 years, 1 month ago

do reeshab u read at fiitjee cuz this problem was given there – Superman Son · 4 years, 2 months ago

@Superman Son – hey! are you in fiitjee? if yes please tell the centre. I am in fiitjee south delhi. – Anoopam Mishra · 4 years, 2 months ago

You all are awesome, Brilliant.org is so cool :D – Reeshabh Ranjan · 3 years, 7 months ago

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

TopNewestWe 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 · 4 years, 2 months ago

Log in to reply

_Hint: _\( 32 = 2^5 \). – Calvin Lin Staff · 4 years, 2 months agoLog in to reply

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 · 4 years, 1 month ago

Log in to reply

do reeshab u read at fiitjee cuz this problem was given there – Superman Son · 4 years, 2 months ago

Log in to reply

– Anoopam Mishra · 4 years, 2 months ago

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

You all are awesome, Brilliant.org is so cool :D – Reeshabh Ranjan · 3 years, 7 months ago

Log in to reply