Given log10 2 = 0.30103, log10 3 = 0.47712. Find the number

Given log₁₀ 2 = 0.30103, log₁₀ 3 = 0.47712. Find the number of digit, in 3¹² x 2⁸ ?

Let N = 3¹² x 2⁸
⇒ log N = 12 x log3 + 8 x log 2
⇒ log N = 12 x 0.47712 + 8 x 0.30103
⇒ log N = 8.13368
∴ No.of digits = 8 + 1 = 9