Question

If 1400=2^a×5^b×7^c then the value of a+b-c=​

Answer 1

Step-by-step explanation:

1400=2^a5^b7^c

2^3×5^2×7^1=2^a×5^b×7^c

a=3,b=2,c=1

a+b-c=3+2-1=4

Answer 2

Given,

$1400 = 2^a * 5^b *7^c$

To Find,

Value of a + b - c = ?

Solution,

By Prime factorization, 1400 can be written as

1400 = 2 x 2 x 2 x 5 x 5 x 7

Exponential form of 1400 = $2^3 * 5^2 * 7^1$

According to question, $1400 = 2^a * 5^b *7^c =2^3 * 5^2 * 7^1$

By comparing this equation ,

a = 3

b = 2

c = 1

Then the value of a + b - c = 3 + 2 - 1  = 4

Hence,  If 1400=2^a×5^b×7^c then the value of a+b-c is 4