Logarithmic Properties and Power Rule

The video tutorial explains how to expand a logarithmic expression, specifically log(343/125), using base 10. It covers the properties of logarithms, such as the division property (log X/Y = log X - log Y) and the power rule (log X^M = M log X). The tutorial demonstrates converting numbers into powers, simplifying expressions by factoring out common terms, and ultimately presenting the expanded form of the given logarithmic expression.

What is the assumed base of a logarithm if no base is specified?

• Base e

• Base 2

• Base 5

• Base 10

What is the base of the logarithm in the expression log(343/125) if not specified?

• Base 5

• Base e

• Base 10

• Base 2

How can the expression log(a/b) be rewritten using logarithmic properties?

• log(a) + log(b)

• log(a) - log(b)

• log(a) * log(b)

• log(a) / log(b)

What is the result of applying the division property to log(343/125)?

• log(343) / log(125)

• log(343) * log(125)

• log(343) + log(125)

• log(343) - log(125)

What is 343 expressed as a power of 7?

• 7^4

• 7^2

• 7^5

• 7^3

What is 125 expressed as a power of 5?

• 5^5

• 5^4

• 5^3

• 5^2

What is the expanded form of log(343) using powers?

• log(7^5)

• log(7^4)

• log(7^2)

• log(7^3)

What is the expanded form of log(125) using powers?

• log(5^4)

• log(5^5)

• log(5^2)

• log(5^3)

What is the logarithmic power rule used in the expansion?

• log(x^m) = m * log(x)

• log(x^m) = log(x) + m

• log(x^m) = log(x) / m

• log(x^m) = log(x) - m

How does the power rule affect the expression log(7^3)?

• log(7) - 3

• log(7) + 3

• log(7) / 3

• 3 * log(7)