If logₓ y = 100 and log₂ x = 10, then what is the value of y?

Correct option is D

Given:

logₓ y = 100

log₂ x = 10
Formula Used:

Change of base formula:

logₐ b = logₖ b / logₖ a

Also, a^{​logₐ b} = b

Solution:

From log₂ x = 10 => x = 2¹⁰
Now use logₓ y = 100

This means: y = x¹⁰⁰ = (2¹⁰)¹⁰⁰ = 2^{​(10 × 100)} = 2¹⁰⁰⁰

Final Answer: (d) 2¹⁰⁰⁰