Aren't the powers too large?

Algebra Level 3

$\large\color{#D61F06}{2^{300} , 3^{200}}$

Find the greater number.

3^{200}

Both

2^{300}

3 solutions

Anuj Shikarkhane
Aug 16, 2015

$2^{300}$ can also be written as $(2^3)^{100}$ .

This is same as $8^{100}$ .

$3^{200}$ can also be written as $(3^2)^{100}$ .

This is same as $9^{100}$ .

$9^{100} > 8^{100}$ .

Therefore $3^{200}$ is greater than $2^{300}$ .

(Upvote if you are satisfied.)

I am satisfied. Upvoted!

Nelson Mandela - 5 years, 10 months ago

Anuj Shikarkhane - 5 years, 10 months ago

Definitely the most simplest solution.Upvoted!

Athiyaman Nallathambi - 5 years, 10 months ago

One of the options is very funny. When you are asking which is greater how can "both" be one of the options?

Kushagra Sahni - 5 years, 10 months ago

Cleres Cupertino
Aug 17, 2015

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

Dev Sharma
Aug 16, 2015

2^300 has 91 digits.

3^200 has 96 digits.

Now 3^200 is greater.

You should try and mention how you got the digits but otherwise a good solution.

Athiyaman Nallathambi - 5 years, 10 months ago

using logarithm, i found the digits

Dev Sharma - 5 years, 10 months ago

I kind of guessed that.But if you had actually written down the method in your solution it would be much better.

Athiyaman Nallathambi - 5 years, 10 months ago