Question

Expand the logarithm fully using the properties of logs. Express the final answer in terms of logx, and logy. log(x)/(y³)

Answer 1

To expand the logarithm log(x/y³), apply the properties of logarithms: separate the quotient into the difference of two logs, and then apply the power rule to the logarithm of y raised to the third power. The final expanded form is log(x) - 3 * log(y).

Step-by-step explanation:

The student has asked to expand the logarithm of log(x/y³) using the properties of logarithms.

According to the properties of logarithms:

1. The logarithm of a quotient log(a/b) is the difference of the logarithms: log a - log b.
2. The logarithm of a number raised to an exponent log(a¾n) is the product of the exponent and the logarithm of the number: n * log a.

Applying these properties:

• First, separate the logarithm of the quotient into the difference of two logarithms: log(x) - log(y³).
• Then, use the power rule to bring down the exponent: 3 * log(y).
• The fully expanded logarithm is: log(x) - 3 * log(y).