Properties of Logarithms. The Product Rule. Let b , M , and N be positive real numbers with b 1. log b (MN) = log b M + log b N The logarithm of a product is the sum of the logarithms. For example, we can use the product rule to expand ln (4 x ): ln (4 x ) = ln 4 + ln x . æ .
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Let b, M, and N be positive real numbers with b 1.
logb (MN) = logbM + logbN
The logarithm of a product is the sum of the logarithms.
For example, we can use the product rule to expand ln (4x):
ln (4x) = ln 4 + ln x.
Let b, M, and N be positive real numbers with b = 1, and let p be any real number.
log bM p = p log bM
The logarithm of a number with an exponent is the product of the exponent and the logarithm of that number.
Write the following as single logarithms:
For any logarithmic bases a and b, and any positive number M,
The logarithm of M with base b is equal to the logarithm of M with any new base divided by the logarithm of b with that new base.