Question

Expand the expression: ln(3x^2y).

Answer 1

To expand the expression ln(3x^2y), use logarithmic properties to separate the product and exponent terms, resulting in ln(3) + 2*ln(x) + ln(y).

Step-by-step explanation:

To expand the expression ln(3x^2y), we will apply logarithmic properties that help simplify the expression. The properties we will use are:

• The logarithm of a product of two numbers is the sum of the logarithms of those two numbers: ln(xy) = ln(x) + ln(y).
• The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number: ln(x^n) = n * ln(x).

Using these properties, we can expand ln(3x^2y) into simpler terms:

1. Apply the first property to separate the terms: ln(3) + ln(x^2y).
2. Separate x^2 and y using the first property again: ln(3) + ln(x^2) + ln(y).
3. Apply the second property to the term x^2: ln(3) + 2*ln(x) + ln(y).

Therefore, the expanded form of ln(3x^2y) is ln(3) + 2*ln(x) + ln(y).