Understanding the Power Rule of Logarithms

This video tutorial explains the power rule of logarithms, which states that log base B of M raised to the power of n equals n times log base B of M. The tutorial demonstrates how to use this property to expand logarithms and write them with a coefficient of one. Examples include expanding log base 7 of X to the 5th and log base 2 of 81. The video also covers reversing the power rule to simplify logarithms, such as converting 3 natural log X to natural log X cubed. The tutorial emphasizes the importance of having a coefficient of one to apply other logarithmic properties.

What is the power rule of logarithms used for?

• To add logarithms

• To expand or condense logarithms

• To divide logarithms

• To multiply logarithms

In the expression log base 7 of X to the 5th power, what does the number 5 represent?

• The base of the logarithm

• The coefficient of the logarithm

• The exponent of the logarithm

• The result of the logarithm

Which property of logarithms is used to expand a logarithm into a sum of logarithms?

• Power property

• Quotient property

• Product property

• Base change property

How can log base 2 of 81 be rewritten using the power rule?

• As log base 2 of 9

• As log base 2 of 3 squared

• As 4 times log base 2 of 3

• As 81 times log base 2 of 3

What is the prime factorization of 81?

• 3 to the power of 4

• 3 times 3

• 9 times 9

• 4 times 3

When using the power rule in reverse, what does a coefficient of one imply?

• The logarithm is multiplied by one

• The logarithm is in its simplest form

• The base is one

• The exponent is one

How can 3 natural log X be rewritten using the power rule?

• As X to the power of 3

• As 3 times X

• As natural log X cubed

• As natural log 3 times X

What is the equivalent expression for log base 3 of the quantity x - 2 raised to the 1/2 power?

• Log base 3 of x - 2 cubed

• Log base 3 of the square root of x - 2

• Log base 3 of x - 2

• Log base 3 of x - 2 squared

What is the significance of writing logarithms with a coefficient of one?

• It changes the base of the logarithm

• It simplifies the logarithm

• It allows the use of product and quotient properties

• It makes the logarithm equal to zero

What is the relationship between rational exponents and square roots in logarithms?

• Square roots are more complex

• They are equivalent expressions

• Rational exponents are always larger

• They are unrelated