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High School Mathematics
3.21 Problems on Logarithms - I

Example:
Prove that, log 35 = log 7 + log 5.
Solution:
Given that,
R.H.S. = log 35
take the factors of 35, that is 35 = 7 * 5
= log (7*5)
= log 7 + log 5 [Since log (ab) = log a + log b]
= LHS.
Therefore, RHS = LHS.

Directions: Prove the following problems. Also write at least ten examples of your own.

1. Prove that, log 22 = log 11 + log 2.

2. Prove that, log 15 = log 5 + log 3.

3. Prove that, log 105 = log 7 + log 5 + log 3.

4. Prove that, log 66 = log 11 + log 3 + log 2.

5. Prove that, log 110 = log 11 + log 5 + log 2.

6. Prove that, log 385 = log 11 + log 7 + log 5.