Understanding Logarithms and Exponential Forms

The video tutorial explains how to evaluate logarithms without a calculator by converting them into exponential form. It covers several examples, including logs with bases 4, 16, 1/3, 3, and 8, demonstrating how to solve them by matching bases or using reciprocal properties. The tutorial also explains simplifying expressions with the same base and log, emphasizing the importance of understanding the relationship between logarithms and exponents.

What is the first step in evaluating a logarithm without a calculator?

• Use a calculator to find the value

• Guess the value of the logarithm

• Convert the logarithm to a fraction

• Rewrite the logarithm in exponential form

What is the value of log base 4 of 64?

• 2

• 3

• 4

• 5

How can 16 be rewritten to have a base of 2?

• 2 to the power of 3

• 2 to the power of 4

• 2 to the power of 5

• 2 to the power of 6

What does a negative exponent indicate?

• A negative number

• A reciprocal

• A zero value

• A complex number

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

• -3

• 3

• 4

• -4

How can 1/9 be expressed using base 3?

• 3 to the power of 2

• 3 to the power of -2

• 3 to the power of -1

• 3 to the power of 1

What is the simplified form of log base 3 of 1/9?

• -3

• 3

• -2

• 2

What happens when a base and a log have the same base?

• The expression doubles

• The expression becomes zero

• The expression simplifies to the exponent

• The expression becomes undefined

How can 8 be rewritten using base 2?

• 2 to the fourth

• 2 cubed

• 2 squared

• 2 to the fifth

What is the value of log base 8 of 4?

• 1/2

• 2/3

• 3/2

• 2