Understanding the Natural Logarithm of a Product | ln(ab) = ln(a) + ln(b)

ln(ab)

In mathematics, the natural logarithm of a product of two numbers, denoted as ln(ab), can be expressed as the sum of the natural logarithms of the individual numbers

In mathematics, the natural logarithm of a product of two numbers, denoted as ln(ab), can be expressed as the sum of the natural logarithms of the individual numbers. The exponential function e (approximately 2.71828) is the base of the natural logarithm.

To calculate ln(ab), you can use the following formula:

ln(ab) = ln(a) + ln(b)

For example, let’s calculate ln(4 × 5):

1. Find ln(4) using a scientific calculator or logarithm table. Let’s say ln(4) ≈ 1.38629.
2. Find ln(5). Let’s say ln(5) ≈ 1.60944.
3. Add ln(4) and ln(5): 1.38629 + 1.60944 ≈ 2.99573.
4. Therefore, ln(4 × 5) ≈ 2.99573.

Note that the natural logarithm provides the exponent to which the base e must be raised to obtain the given number. In this case, ln(4 × 5) represents the exponent to which e must be raised to obtain the value 20.0855 (e^(2.99573) ≈ 20.0855).

Remember that the natural logarithm ln is the inverse function of the exponential function e^x.

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