Question

if log 2=0.30103...then how many digits in 4^2020​

Answer 1

Assume

$x = 4²⁰²⁰</p><p>$

$</p><p>log _{10} (x)=2×2020. log_{10} (2)$

$</p><p>x ≈ 10^{4040 \times 0.30103}$

$x \approx 10 ^{1216.1612}$

So, The number 4²⁰²⁰ has 1217 digits

4²⁰²⁰≈ 1.449×10¹²¹⁶