Find the number of digits in 4^2013 , if log^2 = 0.3010

Open in App

Solution

We know that x has n+1 digits if greatest integer logx has n digits.

Log4^2013= 2013 log2²= 2(2013)log2

=4026(0.3010)

=1211.826 Gratest integer of 1211.86=1211 so

So 4^2013 has 1211+1=1212 digits.

Suggest Corrections

Similar questions

Find the number of digits in 4²⁰¹³. If log₁₀2 = 0.3010

{log}_{10} 2 = 0.3010, {log}_{10} 3 = 0.4771

5^{200}

{log}_{10} 2 = 0.3010

2^{75}

{log}_{10} 2 = 0.3010

2000^{2000}

log 10 (2) = 0.3010

20^{64}

Join BYJU'S Learning Program