Question

answere the following​

Answer 1

Answer:

1212 digits

Step-by-step explanation:

Let x = 4^( 2013 )

⇒ x = ( 2² )^( 2013 )

Using ( a^m )^n = a^mn

⇒ x = 2^( 2 × 2013 )

⇒ x = 2^( 4026 )

Taking log on both sides

⇒ log x = log 2^( 4026 )

Using Power rule log a^m = m. log a

⇒ log x = 4026 × log 2

Given : log 2 = 0.3010

⇒ log x = 4026 × 0.3010

⇒ log x = 1211.826

⇒ log 2^( 2013 ) = 1211.826

Here,

• Characteristic = 1211
• Mantisa = 826

No. of digits = Characteristic + 1 = 1211 + 1 = 1212

Therefore the no. of digits in 4^( 2013 ) are 1212 digits