Maths

[tania]

Hi
Can some one pls explain how to solve this question without log?
Which one is greater: 2^300 or 3^200 ?

Thanks

[Amit Goyal]

2^{300} = 8^{100}
3^{200} = 9^{100}

Therefore, 3^{200} > 2^{300}.

[tania]

Thank you Sir

[Rajat]

2^300 and 3^200.

Divide 3^200 by 2^300.
=> (3/2)^200 * (1/2)^100
= (3/2)^100 * (3/4)^100
= (9/8)^100

This is obviously > 1
=> what we started with: 3^200 / 2^300 > 1
=> 3^200 > 2^300


Hope I didn't make any mistake anywhere