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

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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**

We have to find the value of log(2) 400 - log(2) 100

We use the property: log a - log b = log(a/b)

log(2) 400 - log(2) 100

=> log(2) [ 400/100]

=> log(2) 4

=> log(2) 2^2

use the property that log a^b = b*log a

=> 2*log(2) 2

the log of a number equal the base is 1

=> 2*1

=> 2

**The required value of the expression is 2**