Question

If log_x y = 100 and log₂ x = 10, then the value of y is:
1. 2¹⁰
2. 2¹⁰⁰
3. 2¹⁰⁰⁰
4. 2¹⁰⁰⁰⁰

Answer 1

Correct Answer - Option 3 : 2¹⁰⁰⁰

Concept:

Logarithms: If ax = y, then we say that loga y = x.

Powers: (a^x)^y = a^xy.

Calculation:

Using the definition of logarithms:

log2 x = 10

⇒ x = 2¹⁰.

And, logx y = 100

⇒ y = x¹⁰⁰ = (2¹⁰)¹⁰⁰ = 2^10×100 = 2¹⁰⁰⁰.