Evaluate the given exponential expressions without using a calculator: log2 (400) - log2 (100)

Given that log2 (400) - log2
(100)

We need to find the values of the expression without
using the calculator.

Then we will use logarithm properties
to find the values.

We know that log a - log b = log
a/b

==> log2 (400) - log2 (100 = log2
(400/100)

==> log2 (400) - log2 (100) = log2
(4)

But we know that 4 =
2^2.

==> log2 (4) = log2
2^2

Now we know that log a^b = b*log
a

==> log2 (2^2) = 2*log2 2 = 2*1 =
2

Then the values of log2 (400) -
log2 (100) = 2