Question

find no of digits in 4^2013,if log 2=0.3010

Answer 1

given 4^ 2013
Let us take log 4^2013 
= log[(2)²]^2013    [∵ (a^m)^n = a^mn]
= log 2^ 4026        
= 4026 log2                [∵ logm^n = nlogm] 
= 4026 × 0.301           [∵ log2 = 0.301]
= 1211.826
∴ 4^2013 has 4 digits before decimal

Answer 2

Answer:

1211.826 ~ 1212 digits

Step-by-step explanation:

Number of digits in a^x can be determined by logarithms.

The value of log a^x is the value number of number of digits in a^x.

So, N.o of digits in 4^2013 = log 4^2013

                                            = log 2^4026

                                            = 4026 log 2

                                            = 4026 x 0.3010

                                            = 1211.826 ~ 1212 digits