Using the properties of logarithms to help you expand a logarithmic expression

The video tutorial explains logarithms, focusing on base notation and simplification of expressions. It covers the product rule and emphasizes the importance of using brackets in expressions. The tutorial concludes with a final expression, demonstrating the application of these concepts.

What is the assumed base of a logarithm if it is not explicitly written?

• 5

• e

• 2

• 10

Which rule is used to separate the terms in the expression log(XY^4)?

• Quotient Rule

• Power Rule

• Product Rule

• Chain Rule

How is the expression log(XY^4) broken down using the product rule?

• log X + log Y^4

• log X * log Y^4

• log X - log Y^4

• log X / log Y^4

Why is it important to use brackets in logarithmic expressions involving quotients?

• To denote terms in the numerator

• To make the expression look complex

• To simplify the expression

• To denote terms in the denominator

What is the final expression for log(3) minus log(XY^4) when simplified?

• log(3) - log(X) - 4log(Y)

• log(3) + log(X) + 4log(Y)

• log(3) - (log(X) + 4log(Y))

• log(3) + (log(X) - 4log(Y))