Expanding logarithms with parenthesis

The video tutorial explains how to expand logarithms using specific rules. It covers three main properties: the product rule, the quotient rule, and the power rule. The instructor demonstrates how to apply these rules to break down complex logarithmic expressions into simpler components. Common mistakes made by students are highlighted, and solutions are provided to avoid these errors. The tutorial emphasizes the importance of using parentheses correctly and applying the distributive property when necessary.

Which of the following is the correct expansion of log base X of (M * N)?

• log base X of M * log base X of N

• log base X of M / log base X of N

• log base X of M - log base X of N

• log base X of M + log base X of N

When expanding log base 5 of (X^2 / (Y^2 * Z^3)), what is the first step?

• Add log base 5 of X^2 and log base 5 of Y^2

• Divide log base 5 of X^2 by log base 5 of Y^2

• Subtract log base 5 of Y^2 * Z^3 from log base 5 of X^2

• Multiply log base 5 of X^2 by log base 5 of Y^2

Why is it important to use parentheses when expanding log base 5 of (X^2 / (Y^2 * Z^3))?

• To avoid subtracting the wrong terms

• To make the expression look neater

• To simplify the expression further

• To ensure the correct order of operations

What is the result of applying the distributive property to the expression log base 5 of (X^2) - log base 5 of (Y^2 * Z^3)?

• 2 log base 5 of X + 2 log base 5 of Y + 3 log base 5 of Z

• 2 log base 5 of X - 2 log base 5 of Y - 3 log base 5 of Z

• log base 5 of X^2 - log base 5 of Y^2 - log base 5 of Z^3

• log base 5 of X^2 + log base 5 of Y^2 + log base 5 of Z^3

What is the final expanded form of log base 5 of (X^2 / (Y^2 * Z^3)) after applying all the rules?

• 2 log base 5 of X + 2 log base 5 of Y + 3 log base 5 of Z

• log base 5 of X^2 - log base 5 of Y^2 - log base 5 of Z^3

• 2 log base 5 of X - 2 log base 5 of Y - 3 log base 5 of Z

• log base 5 of X^2 + log base 5 of Y^2 + log base 5 of Z^3