Exploring Properties of Logarithms

What does the product rule of logarithms allow us to do?

• Solve logarithmic equations

• Expand a single logarithm into a multiplication of two separate logarithms

• Condense a multiplication inside a logarithm into a sum of two logarithms

• Divide two logarithmic expressions

When condensing logarithms, what is a necessary condition for the bases?

• The bases must be different

• The bases must be prime numbers

• The bases must be the same

• There is no condition on the bases

What is the result of condensing log base 3 of 9 plus log base 3 of 5?

• log base 3 of 14

• log base 3 of 9 times 5

• log base 3 of 45

• log base 3 of 15

What does condensing a logarithmic expression involve?

• Combining multiple logarithms into a single logarithm

• Splitting a single logarithm into multiple logarithms

• Applying the logarithm to each term inside the expression separately

• Changing the base of the logarithm

How do you expand log base 5 of (x^2 - 4)?

• log base 5 of x plus log base 5 of 2

• log base 5 of (x + 2) times (x - 2)

• log base 5 of (x + 2) plus log base 5 of (x - 2)

• log base 5 of x minus log base 5 of 4

What does the quotient property of logarithms state?

• It allows multiplication inside a logarithm to be written as the sum of two logarithms

• It simplifies logarithmic expressions without changing their bases

• It allows division inside a logarithm to be written as the difference of two logarithms

• It allows division inside a logarithm to be written as the sum of two logarithms

What is the simplified form of the natural log of 96 divided by 6?

• The natural log of 6

• The natural log of 90

• The natural log of 16

• The natural log of 96

What is the effect of applying the quotient property to log base 7 of the square root of 40 over the square root of 5?

• log base 7 of 5

• log base 7 of 8

• log base 7 of the square root of 35

• log base 7 of the square root of 8

What is the result of applying the power property to log base 10 of 6 raised to the third power?

• log base 10 of 6 divided by 3

• 3 times log base 10 of 6

• log base 10 of 18

• log base 10 of 216

How can the cube root be rewritten using exponents in logarithmic expressions?

• As the argument raised to the power of 1/3

• As the argument divided by 3

• As the argument multiplied by 3

• As the argument raised to the power of 3