Regret using calculator

Algebra Level 3

$\large \color{#20A900}{A=2^{1465}} , \ \ \ \ \ \color{#3D99F6}{B=3^{1172}} , \ \ \ \ \ \color{#D61F06}{C=5^{879}}$

If these numbers are arranged from smallest to biggest in ascending order, what would the order of arrangement be?

C,B,A C,A,B A,C,B B,A,C B,C,A A,B,C

2 solutions

Curtis Clement
May 14, 2015

$\ gcd(1465,1172, 879) = 293$ such that: $\ A = (2^5)^{293} = 32^{293}$ $\ B = (3^4)^{293} = 81^{293}$ $\ C = (5^3)^{293} = 125^{293}$ $\therefore\large { A < B < C }$

Moderator note:

Just for the sake of clarity, can you explain how you calculate " $\ gcd(1465,1172, 879) = 293$ "?

$1465-1172=1172-879=293$ Since 293 divides 879, it divides 1172 and 1465 as well.

BK Lim - 6 years ago

Good solution I thought of that but just to try another method I did it with logarithms to base 10 .

shivamani patil - 5 years, 11 months ago

Peter Michael
Jun 10, 2017

Divisible power

Two nine three is G C D

Then compare bases

Regret using calculator

2 solutions

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