Expanding Logarithmic Expressions Quiz

What is the result of applying the product rule to log base 4 of 7x?

• log base 4 of 7 + log base 4 of x

• log base 4 of 7 - log base 4 of x

• log base 4 of 7x + 1

• log base 4 of 7x

How does the quotient rule expand log base 7 of x/y?

• log base 7 of x + log base 7 of y

• log base 7 of x - log base 7 of y

• log base 7 of x * log base 7 of y

• log base 7 of x / log base 7 of y

What happens to the exponent in the power rule for logarithms?

• It is divided by the logarithm

• It is multiplied at the beginning of the logarithm

• It is subtracted from the logarithm

• It is added to the logarithm

How would you expand ln(e^3/7) using the power and quotient rules?

• ln(e) + 3 ln(7)

• 3 ln(e) - ln(7)

• ln(e) - 3 ln(7)

• 3 ln(e) + ln(7)

What is the expanded form of ln(sqrt(x))?

• ln(x^2)

• 2 ln(x)

• ln(x)/2

• 1/2 ln(x)

When expanding log base b of (x^2 * sqrt(y)), what is the first step?

• Apply the power rule to x^2

• Apply the product rule

• Simplify the expression

• Apply the quotient rule

How do you express cube root of x as an exponent?

• x^2

• x^(1/3)

• x^3

• x^(3/2)

What is the expanded form of log base 5 of (cube root of x / 25)?

• 1/3 log base 5 of x + 2 log base 5 of 5

• 1/3 log base 5 of x - 2 log base 5 of 5

• log base 5 of x + 1/3 log base 5 of 25

• log base 5 of x - 1/3 log base 5 of 25

In the expression log base 6 of (x^2/36), what is the result of applying the power rule?

• log base 6 of x^2 + 2 log base 6 of 6

• 2 log base 6 of x + log base 6 of 36

• log base 6 of x^2 - 2 log base 6 of 6

• 2 log base 6 of x - log base 6 of 36

What is the final step in expanding logarithmic expressions?

• Divide all terms by the base

• Add all terms together

• Bring exponents to the front of the log function

• Multiply all terms by the base