Awithout using the calculator find the integer such that N

A/without using the calculator, find the integer such that : N < log2 (45) <N+1.
Show in detal why N < log2 (45) <N+1.

B/ use the change of these formula with ln to rewrite log2 (45)

c/ use a colculator to find log2 (45) correct 4 decimal places

Solution

N < log2 (45) <N+1

we can write : y = logxA ----> x^y = A

So, 2^N < 45 < 2^(N+1)

2^N =2^5 = 32

2^(N+1) = 64

So, 32<45<64

So. N = 5

y = log2(45)

Use the log property: logx(y) = logy/logx

= log45/log2

=1.6532/0.30103

= 5.4918