Logarithmic Expressions Quiz

The video tutorial explains how to solve a complex logarithmic expression using the change of base formula and properties of logarithms. It begins by introducing the problem and encourages viewers to attempt solving it. The instructor then explains the change of base formula, demonstrating how to convert logarithms to a common base. Next, the video covers simplifying expressions by converting numbers to powers and applying logarithmic properties to simplify further. Finally, the instructor performs the final calculations, arriving at the solution and presenting it as both an improper fraction and a mixed number.

What is the expression that needs to be evaluated in the problem?

• log base 10 of 27 times log base 36 of 32 times log base 9 of 216

• log base 16 of 27 times log base 36 of 32 times log base 9 of 216

• log base 16 of 27 times log base 10 of 32 times log base 9 of 216

• log base 16 of 27 times log base 36 of 32 times log base 10 of 216

What is the change of base formula for logarithms?

• log base a of b = log a / log b

• log base a of b = log b * log a

• log base a of b = log b / log a

• log base a of b = log a * log b

Which base is typically chosen when using the change of base formula?

• Base 2

• Base 5

• Base 10

• Base 20

How can the number 27 be expressed in terms of powers of smaller numbers?

• 5 to the power of 2

• 2 to the power of 4

• 3 to the power of 3

• 6 to the power of 2

What is the logarithmic property that allows exponents to be moved to the front?

• log a^b = a log b

• log a^b = log a - log b

• log a^b = b log a

• log a^b = log a + log b

What happens to the expression after applying the logarithmic property and canceling terms?

• It becomes 5/3 times 2/4 times 2/3

• It becomes 3/5 times 4/2 times 2/3

• It becomes 3/4 times 5/2 times 3/2

• It becomes 4/3 times 2/5 times 2/3

What is the result of multiplying the remaining coefficients in the expression?

• 32/13

• 16/45

• 13/32

• 45/16

How is the improper fraction 45/16 converted into a mixed number?

• 2 16/13

• 3 13/16

• 2 13/16

• 3 16/13

What is the final answer for the original problem?

• 3 16/13

• 2 16/13

• 3 13/16

• 2 13/16

Which property of logarithms is used to simplify the expression?

• Change of base formula

• Product rule

• Quotient rule

• Power rule