Question

If log₂ y = x, log₃ z = x, express 12^x in terms of y and z.

Answer 1

Given: Let log₂ y = x and log₃ z = x so y = 2^x and z = 3^x.

Step-wise calculation:

From log₂ y = x

⇒ y = 2^x

So 2^x = y.

From log₃ z = x

⇒ z = 3^x

So 3^x = z.

12^x = (3 × 4)^x 

12^x = 3^x × 4^x

12^x = 3^x × (2²)^x

12^x = 3^x × 2^2x

12^x = z × (2^x)² 

12^x = z × y²

12^x = y²z