Question

please answer the question​

Answer 1

Solution :

Given,

log₁₀a = 2x + y

⇒ 3 log₁₀a = 3 (2x + y) = 6x + 3y

⇒ log₁₀a³ = 6x + 3y

& log₁₀b = x - 2y

⇒ 2 log₁₀b = 2 (x - 2y)

⇒ log₁₀b² = 2x - 4y

∴ log₁₀(10a³ / b²)

= log₁₀(10a³) - log₁₀(b²)

= log₁₀10 + log₁₀a³ - log₁₀b²

= 1 + (6x + 3y) - (2x - 4y)

= 1 + 6x + 3y - 2x + 4y

= 1 + 4x + 7y ,

which is in terms of x and y.