List 3 numbers in ascending order

Algebra Level 2

Without using a calculator , arrange $3^{50}$ , $4^{40}$ , and $5^{30}$ in ascending order.

5^{30} < 4^{40} < 3^{50}

5^{30} < 3^{50} < 4^{40}

They are all equal

3^{50} < 4^{40} < 5^{30}

None of the others

1 solution

Ethan Mandelez
Feb 29, 2020

Notice that the powers of those numbers are multiples of 10.

3^50 = 3^(5x10) = 243^10,
4^40 = 4^(4x10) = 256^10,
5^30 = 5^(3x10) = 125^10

Therefore 5^30 < 3^50 < 4^40

Easy...... I like it though. Probability of the correct answer was 20 % ! haha.

Nikola Alfredi - 1 year, 3 months ago

Glad you liked it ^_^

Ethan Mandelez - 1 year, 1 month ago