Question

Hey it be great if someone could help with work!

2. Given log2 7 ≈ 2.8074 and log2 9 ≈ 3.1699, evaluate the expressions.
(a) log2 3
(b) log2 (28/9)

Answer 1

`log_(2)(7) = 2.8074`

`log_(2)(9) = 3.1699`

a)

`log_(2)(3) = log_(2)( {9}^{ (1)/(2) } ) = (1)/(2) log_(2)(9) = (1)/(2) (3.1699) = 1.5845`

b)

`log_(2)( (28)/(9) )`

`= log_(2)(28) - log_(2)(9)`

`= log_(2)( {2}^(2) * 7 ) - log_(2)(9)`

`= 2 log_(2)(2) + log_(2)(7) - log_(2)(9)`

`= 2 + 2.8074 - 3.1699`

`= 1.6375`