Logarithmic Properties and Evaluations

The video tutorial covers the properties and applications of logarithms, including the product, division, and exponent rules. It explains how to express logarithms in terms of others, evaluate logarithmic expressions, and condense them. The change of base formula is also discussed, providing methods to calculate logarithms using different bases.

What is the value of log base 5 of 5?

• 0

• 1

• 10

• 5

Which of the following is true about the natural log of a negative number?

• It is undefined

• It is negative

• It is zero

• It is positive

What is the product property of logarithms?

• log base B of x + y

• log base B of x * y = log base B of x + log base B of y

• log base B of x / y = log base B of x - log base B of y

• log base B of x^y = y * log base B of x

How can you express log base B of x^P using the power rule?

• P * log base B of x

• P + log base B of x

• log base B of x + P

• log base B of x^P

How can log of 96 be expressed in terms of log of 2 and log of 3?

• log of 2 + 5 log of 3

• log of 3 + 5 log of 2

• log of 3 - 5 log of 2

• 5 log of 3 + log of 2

What is the expression for log of 32 over 9 in terms of log 2 and log 3?

• 5 log 2 + 2 log 3

• 5 log 2 - 2 log 3

• 2 log 2 - 5 log 3

• 2 log 2 + 5 log 3

How can you evaluate log base 6 of 4 using the change of base formula?

• log of 6 - log of 4

• log of 4 * log of 6

• log of 6 / log of 4

• log of 4 / log of 6

What is the result of evaluating log base 1/3 of 8?

• -0.893

• 0.893

• -1.893

• 1.893

What is the expanded form of natural log of 4M^3N^5?

• ln(4) - 3ln(M) - 5ln(N)

• ln(4) * 3ln(M) * 5ln(N)

• ln(4) / 3ln(M) / 5ln(N)

• ln(4) + 3ln(M) + 5ln(N)

How do you condense 12 log base 4 x - 3 log base 4 x - 2?

• log base 4 of x^12 + x^3

• log base 4 of x^12 / x^3

• log base 4 of x^12 * x^3

• log base 4 of x^12 - x^3