Algebra 2 - Evaluating a Logarithm to a Rational Base

The video tutorial explains how to convert logarithmic expressions into exponential form, focusing on the example of log base 1/2 equals 256. It discusses the concept of negative exponents and how they are used to convert fractions into whole numbers. The tutorial walks through calculating powers of two to determine the correct exponent needed to achieve a specific result. The lesson concludes with a summary and a promise of practice problems to reinforce the concepts learned.

What is the exponential form of the logarithmic expression log to the 1/2 = 256?

• 1/2 raised to the power of 256

• 256 raised to the power of 1/2

• 256 raised to what power equals 1/2

• 1/2 raised to what power equals 256

Why is a negative exponent necessary when converting a fraction to a whole number?

• Because it adds to the fraction

• Because it keeps the fraction the same

• Because it inverts the fraction

• Because it makes the fraction larger

What is the result of 1/2 raised to the negative first power?

• 1/2

• 1

• 2

• 4

Which power of 2 equals 256?

• 2 to the 8th power

• 2 to the 6th power

• 2 to the 7th power

• 2 to the 9th power

What is the correct exponent for 1/2 to equal 256 when raised to a power?

• -6

• -7

• -8

• -9