Can We Compare Them?

Algebra Level 1

Which huge number is greater? $\large {\color{#20A900}{2^{41}} ~~~~\text {or}~~~~\color{#3D99F6}{3^{24}}}$

3^{24}

2^{41}

2 solutions

Otto Bretscher
Nov 2, 2015

$2^{41}>2^{40}=32^8>27^8=3^{24}$

Alter. Take log base 10

Dev Sharma - 5 years, 7 months ago

That is the shortest answer.

Prasit Sarapee - 5 years, 7 months ago

Mohamud Elmi
Nov 5, 2015

we can see the ratio of the 41:24 =4:x and x will equal to 2 hence 2 to the power of 4 is larger than 3 to the power of 2

by logarithms log $2^{41}$ =41log2 which is aproximately equal to 12.341. so it has 13 digits. log $3^{24}$ =24log2 which is aproximately equal to 11.4504.so it has 12 digits. that is why $2^{41}$ is more.

sai aryanreddy - 5 years, 7 months ago

Can We Compare Them?

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