49th Problem 2016

Algebra Level 2

Which is larger?

$\Large 7^{3690} \text{ or }11^{2016} \; .$

11^{2016}

7^{3690}

2 solutions

Hung Woei Neoh
May 11, 2016

$\log_{10} 7^{3690} = 3690 \log_{10}7 \approx 3118.41\\ \log_{10} 11^{2016} = 2016 \log_{10} 11 \approx 2099.45$

From here, we know that:

$\log_{10} 7^{3690} > \log_{10} 11^{2016}\\ \implies 7^{3690} > 11^{2016}$

The larger number is $\boxed{7^{3690}}$

How do you get the logarithm so fast? Is it some property I am not aware of or just calculator

Adrian Ma - 11 months, 1 week ago

展豪張
Mar 26, 2016

Take the logarithm of them and then compare.