If log_x y = 100 and log₂ x = 10, find y.

Concept / Approach

• From log₂x = 10 ⇒ x = 2¹⁰.
• From log_xy = 100 ⇒ y = x¹⁰⁰.

Step-by-step calculation
x = 2¹⁰ = 1024y = x¹⁰⁰ = (2¹⁰)¹⁰⁰ = 2¹⁰⁰⁰Therefore, y = 2¹⁰⁰⁰

Check
log_xy = log_2¹⁰2¹⁰⁰⁰ = 1000/10 = 100 ✔