Question

If log₂ x = a and log₅ y = a, then `100^(3a - 1)` is equal to ______.

Options

• `(x^6y^6)/100`

• `(x^3y^3)/100`

• `(x^2y^2)/100`

• `(xy)/100`

Answer 1

If log₂ x = a and log₅ y = a, then `100^(3a - 1)` is equal to `underlinebb((x^6y^6)/100)`.

Explanation:

log₂ x = a 

⇒ x = 2^a

And log₅ y = a 

⇒ y = 5^a

`100^(3a - 1)`

= `(10^2)^(3a - 1)` 

= `10^(6a - 2)` 

= `10^(6a)/100`

= `(2^(6a) xx 5^(6a))/100` 

= `(x^6y^6)/100`