Logarithmic Functions and Exponents

This video tutorial explains how to rewrite equations in logarithmic form. It covers three examples with different bases: 2, 8, and 9. Each example demonstrates the process of converting an exponential equation into its logarithmic equivalent, highlighting the relationship between the base, exponent, and result. The video concludes with a summary of the concepts covered.

What is the purpose of rewriting equations in logarithmic form?

• To simplify multiplication

• To express exponential relationships

• To convert fractions to decimals

• To solve linear equations

In the context of logarithms, what does the 'base' refer to?

• The number of times the base is used as a factor

• The number that is raised to a power

• The result of the exponentiation

• The number being multiplied

How would you express 2^4 = 16 in logarithmic form?

• log base 16 of 2 equals 4

• log base 4 of 2 equals 16

• log base 2 of 4 equals 16

• log base 2 of 16 equals 4

What is the logarithmic form of 2^4 = 32?

• log base 2 of 32 equals 4

• log base 2 of 16 equals 4

• log base 32 of 2 equals 4

• log base 4 of 2 equals 32

In the equation log base 2 of 32 equals 4, what is the exponent?

• 4

• 8

• 32

• 2

How do you express 8^-1 = 1/8 in logarithmic form?

• log base 8 of -1 equals 1/8

• log base 1/8 of 8 equals -1

• log base -1 of 8 equals 1/8

• log base 8 of 1/8 equals -1

What does a negative exponent indicate in logarithmic form?

• A multiplication

• A subtraction

• A division

• An addition

In the equation log base 8 of 1/8 equals -1, what is the base?

• 1/8

• 0

• 8

• -1

How would you express 9^(1/2) = 3 in logarithmic form?

• log base 9 of 1/2 equals 3

• log base 1/2 of 9 equals 3

• log base 3 of 9 equals 1/2

• log base 9 of 3 equals 1/2

What does a fractional exponent represent in logarithmic form?

• A square root

• A cube root

• A multiplication

• A division