Question

Check rithms to expand log(x^(3)z). olve only one variable and should not have any exp are positive.

Answer 1

To expand log(x^3z), one should apply the power rule to bring down the exponent, resulting in 3 · log(x), and then use the multiplication rule to split the logarithm of the product into a sum, yielding the final form as 3 · log(x) + log(z).

Step-by-step explanation:

To expand the logarithmic expression log(x^3z), we can utilize logarithmic properties. The logarithm of a number raised to an exponent can be simplified by bringing the exponent in front of the logarithm. Additionally, when we have a product inside the logarithm, we can split it into a sum of logarithms.

Steps to Expand log(x^3z)

1. Apply the power rule for logarithms which states that log(a^n) = n · log(a). For our expression, the power rule can be applied to x^3 to get 3 · log(x).
2. Utilize the multiplication rule for logarithms which indicates that log(ab) = log(a) + log(b). Therefore, log(x^3z) can be written as log(x^3) + log(z).
3. Combine both properties to get the final expanded form, which is 3 · log(x) + log(z).

This expansion assumes all variables represent positive numbers since logarithms are only defined for positive arguments.