Given that log2=0.3010 and log3=0.4771. calculate without using mathematical table or calculator to find the value of log 0.24

Answer 1

We can use logarithmic properties to solve this problem without a calculator or mathematical table.

Let's first convert 0.24 into a power of 10 by multiplying by 100:
0.24 * 100 = 24

Now, let's express 24 as a product of powers of 2 and 3. We can do this by repeatedly dividing 24 by 2 and 3 until we can't divide anymore:

24 divided by 2 = 12
12 divided by 2 = 6
6 divided by 2 = 3
3 divided by 3 = 1

This means 24 can be expressed as 2 * 2 * 2 * 3.

Now, let's rewrite log0.24 using the properties of logarithms:
log0.24 = log(2 * 2 * 2 * 3)
= log2 + log2 + log2 + log3

Using the given values of log2 and log3:
log2 + log2 + log2 + log3 = 0.3010 + 0.3010 + 0.3010 + 0.4771
= 1.1841

Therefore, log0.24 = 1.1841.