Question

If =100 and =10, find the value of y

Answer 1

The value of y is 3.

Step-by-step explanation:

Given : Expression (100)^2\times (10)^5=(1000)^y(100)

2

×(10)

5

=(1000)

y

To find : The value of y ?

Solution :

Solving the expression as,

(100)^2\times (10)^5=(1000)^y(100)

2

×(10)

5

=(1000)

y

(10^2)^2\times (10)^5=(10^3)^y(10

2

)

2

×(10)

5

=(10

3

)

y

(10)^4\times (10)^5=(10)^{3y}(10)

4

×(10)

5

=(10)

3y

(10)^9=(10)^{3y}(10)

9

=(10)

3y

Comparing the base,

9=3y9=3y

y=\frac{9}{3}y=

3

9

y=3y=3

Therefore, the value of y is 3.