Understanding Logarithms

This video tutorial introduces the properties and notation of logarithms, including special bases like 10 and e. It explains how to convert logarithms to exponential form and solve logarithmic equations. The tutorial covers key logarithmic properties such as the product, quotient, and power rules, and demonstrates how to expand logarithmic expressions using these rules.

What is the base in the expression log base B of x equals y?

• B

• y

• log

• x

How is log base 10 of x commonly written?

• log10(x)

• log(x)

• ln(x)

• log base 10 of x

What is the natural logarithm of x denoted as?

• log base 10 of x

• log(x)

• log base e of x

• ln(x)

If log base 10 of 100 equals x, what is the value of x?

• 10

• 100

• 1

• 2

What is the value of x in log base 2 of 8 equals x?

• 4

• 3

• 2

• 1

What does the product rule for logarithms state?

• Products become quotients

• Products become differences

• Products become products

• Products become sums

According to the quotient rule, how does division inside a logarithm transform?

• Into division

• Into subtraction

• Into multiplication

• Into addition

What does the power rule for logarithms allow you to do with exponents?

• Multiply them by the base

• Add them to the base

• Bring them out front as multiplication

• Divide them by the base

In the expression log base 3 of x squared times y plus 1 over Z cubed, what is the first step in expanding it?

• Use the quotient rule

• Use the power rule

• Use the base change rule

• Use the product rule

When expanding log base 3 of x squared, what happens to the exponent?

• It stays the same

• It is added to the base

• It is subtracted from the base

• It is brought out front as a coefficient