Question

if 2160=2power a*3power b*5power c find value of a b c

Answer 1

We have
2160 = 2 x 1080
= 2 x 2 x 540
= 2 x 2 x 2 x 270
= 2 x 2 x 2 x 2 x 135
= 2 x 2 x 2 x 2 x 3 x 45
= 2 x 2 x 2 x 2 x 3 x 3 x 15
= 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5

thus 2160 = 2⁴ x 3³ x 5

2^a 3^b 5^c = 2160 (given)

so, 2^a 3^b 5^c = 2⁴ x 3³ x 5

^{taking the exponent both sides}

we can say a=4, b=3, c=1 Ans.