Question

If 21168=2^a 3^b 7^c where a, b and c are natural numbers then what is value of 4a-5b+c ?

Answer 1

The value of 4a - 5b + c is 3.

Step-by-step explanation:

We have,

$21168=2^{a} 3^{b} 7^{c}$     ...(1)

To find, $4a-5b+c=?$

∴ 21168 = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 7 × 7

=$2^{4} 3^{3}7^{2}$               ...(2)

From (1) and (2), we get

$2^{a} 3^{b} 7^{c}=2^{4} 3^{3}7^{2}$

Equating powers of a, b and c, we get

$2^{a}=2^{4}$ ⇒ a = 4

$3^{b} =3^{3 }$⇒ b = 3 and

$7^{c}=7^{2}$     ⇒ c = 2

∴  $4a-5b+c=4\times 4-5\times 3+2=3$

Hence, the value of 4a - 5b + c is 3.