If log₂x = a and log₅y = a, write 100^{2a - 1} in terms of x and y.

Given,

log₂x = a and log₅y = a

⇒ x = 2^a and y = 5^a

100^{2a - 1} = 100^2a.100^-1

= (100^a)².100^-1

= [(2².5²)^a]².100^-1

= [(2^2a).(5^2a)]².100^-1

= [(2^a)².(5^a)²]².(100)^-1

= [x².y²]².100^-1

= $\dfrac{x^4y^4}{100}$.

Hence, 100^{2a - 1} = $\dfrac{x^4y^4}{100}$.