Exploring Properties of Logarithms

What does the product property of logarithms state?

• log_b(x^y) = y * log_b(x)

• log_b(x/y) = log_b(x) + log_b(y)

• log_b(xy) = log_b(x) - log_b(y)

• log_b(xy) = log_b(x) + log_b(y)

How do you apply the power property in logarithms?

• log_b(x^y) = log_b(x) - log_b(y)

• log_b(x^y) = log_b(x) + log_b(y)

• log_b(x^y) = y * log_b(x)

• log_b(x^y) = log_b(xy)

What is the result of fully expanding ln(4m^3n^5)?

• ln(4) + ln(m^3) + ln(n^5)

• ln(4) * 3ln(m) * 5ln(n)

• ln(4) + 3ln(m) + 5ln(n)

• 3ln(4) + 5ln(mn)

When expanding log_b(x/y), which property is used?

• Power property

• Change of base formula

• Quotient property

• Product property

How do you condense log_a(x) + log_a(y) into a single logarithm?

• log_a(x/y)

• log_a(xy)

• log_a(x^y)

• log_a(x) - log_a(y)

What is the result of condensing ln(x^(-2)) + ln(x+3) + ln(x)?

• ln(x(x+3)/x^2)

• ln((x+3)/x)

• ln(x^2(x+3))

• ln((x+3)x/x^2)

What is the simplified form of log base 2 of 32?

• 5

• 10

• 2

• 1

What is the value of log_3(81) using the power property?

• 3

• 4

• 1/3

• 9

What does the change of base formula allow you to do?

• Solve logarithmic equations more easily

• Combine two logarithms into one

• Expand a single logarithm into multiple terms

• Convert a logarithm to a different base

How do you solve log_b(x) = y for x?

• x = log_b(y)

• x = b + y

• x = b^y

• x = y/b