Exponents and Logarithm Properties

The video tutorial introduces logarithms and their relationship with exponents. It explains key logarithm properties, such as the addition and subtraction properties, and demonstrates these properties with examples. The tutorial aims to provide an intuitive understanding of how logarithms work and their practical applications.

What is the relationship between exponents and logarithms?

• They are completely unrelated.

• Logarithms are the inverse of exponents.

• Exponents are the inverse of logarithms.

• They are both used to calculate square roots.

Which of the following is a correct representation of the first logarithm property?

• log_b(a) + log_b(c) = log_b(a*c)

• log_b(a) + log_b(c) = log_b(a/c)

• log_b(a) * log_b(c) = log_b(a+c)

• log_b(a) - log_b(c) = log_b(a*c)

In the example provided, what is the result of log base 2 of 8 plus log base 2 of 32?

• log base 2 of 16

• log base 2 of 256

• log base 2 of 64

• log base 2 of 128

What exponent rule is used to explain the first logarithm property?

• Divisive exponent rule

• Subtractive exponent rule

• Additive exponent rule

• Multiplicative exponent rule

What is the second logarithm property?

• log_b(a) + log_b(c) = log_b(a*c)

• log_b(a) - log_b(c) = log_b(a/c)

• log_b(a) / log_b(c) = log_b(a-c)

• log_b(a) * log_b(c) = log_b(a+c)

In the example for the second property, what is the result of log base 3 of 1/9 minus log base 3 of 81?

• log base 3 of 1/81

• log base 3 of 1/243

• log base 3 of 1/27

• log base 3 of 1/729

What is the exponent of 3 that results in 1/9?

• 3

• -2

• 2

• -3

What is the exponent of 3 that results in 81?

• 5

• 6

• 4

• 3

What is the result of subtracting log base 3 of 81 from log base 3 of 1/9?

• -6

• 6

• -4

• 4

What is the equivalent positive exponent of 3 that results in 729?

• 6

• 5

• 7

• 8