Can you compare them

Algebra Level 3

Which of the following four numbers is the largest $3^{210}$ , $7^{140}$ , $17^{105}$ and $31^{84}$ .

They all are equal.

3^{210}

7^{140}

17^{105}

31^{84}

1 solution

Pulkit Gupta
Nov 21, 2015

One way to do this question is to use same base logarithms to compare the numbers,

We take here log to the base 2.

Ex : log_2 $3^{210}$ = 210 log_2 3 Since 1< log_2 3 <2 , therefore 210 < 210 log_2 3 < 420

Similarly, we can compare other numbers.

did the same way.!

Raghav Rathi - 5 years, 6 months ago