Logarithm – properties (logarithms of a division between two numbers and the difference of two logarithms with same base) – pg.5/10
pg. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
4. Logarithm of a division between two numbers and the difference of two logarithms with same base.
The logarithm of a division between two numbers is equal with the difference of the numbers’ logarithmic expression.
The difference of two logarithmic expressions is the reverse to the logarithms of a division.
If we divide the exponential expressions in [4], pg.3, we have: or we can write:
[10] (see Exponents (Powers) §3)
By transforming the exponential expression [10] into a logarithmic expression, we have:
From [3], pg.3, we have:
This means that:
[11] (logarithm of division)

OR
[12] (difference of logarithms)

Example:

(division)

(subtraction)
pg. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
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