Logarithmic Properties and Rules

The video tutorial provides practice on expanding logarithms using various properties. It covers the log of a product, power rule, and quotient rule through multiple problems. The tutorial also explains how to handle exponents and multiple variables in logarithmic expressions, emphasizing the application of these rules in solving problems.

What is the result of expanding the natural log of a product, ln(A * B)?

• ln(A) + ln(B)

• ln(A) * ln(B)

• ln(A) - ln(B)

• ln(A) / ln(B)

What is the expanded form of ln(A * B) using the product rule?

• ln(A) * ln(B)

• ln(A) + ln(B)

• ln(A) - ln(B)

• ln(A) / ln(B)

Which property allows you to bring an exponent down in a logarithmic expression?

• Product Rule

• Quotient Rule

• Change of Base Rule

• Power Rule

How do you express 5 * log(6/11) using logarithmic properties?

• 5 * (log(6) + log(11))

• 5 * (log(6) - log(11))

• log(6^5) - log(11^5)

• log(6/11)^5

How would you expand log(2^4) - log(5) using logarithmic properties?

• log(2^4) - 5 * log(5)

• log(2^4) + log(5)

• 4 * log(2) - log(5)

• 4 * log(2) + log(5)

What is the result of applying the power rule to log(2^4)?

• log(2) * 4

• log(2^4)

• log(2) + 4

• 4 * log(2)

What is the expanded form of log(x * y * z) raised to the power of 1/3?

• log(x) + log(y) + log(z)

• 1/3 * (log(x) + log(y) + log(z))

• log(x * y * z) / 3

• 1/3 * (log(x) * log(y) * log(z))

Which rule is used to expand log(x/y) into a difference of logs?

• Product Rule

• Power Rule

• Change of Base Rule

• Quotient Rule

If you have log(u) - log(v^5), what is the original expression before applying the quotient rule?

• log(u / v^5)

• log(u * v^5)

• log(u) + log(v^5)

• log(u^5 / v)

How can you rewrite log(x * y * z) when raised to the power of 1/3?

• log(x) + log(y) + log(z)

• 1/3 * (log(x) + log(y) + log(z))

• log(x * y * z) / 3

• log(x) * log(y) * log(z)