Question

solve this problem
solve
​

Answer 1

Answer:

The number of digits in 4²⁰¹³ are 1212.

Step-by-step explanation:

Let x = 4²⁰¹³

On taking log₁₀ both sides we get,

log₁₀(x) = log₁₀(4²⁰¹³)

or log₁₀(x) = 2013 * log₁₀(4)

or log₁₀(x) = 2013 * log₁₀(2²)

or log₁₀(x) = 2013 * 2 * log₁₀(2)

or log₁₀(x) = 2013 * 2 * 0.3010

or log₁₀(x) = 1211.826

⇒ The characteristic of log₁₀(x) = log₁₀(4²⁰¹³) is 1211.

⇒ The number of digits in 4²⁰¹³ = 1211+1 = 1212

Formulas used :-

1) log₁₀(aᵇ) = b * log₁₀(a)