Logarithms Quiz

What is the result of applying the product law to log(3X) base a?

• log(3) base a + log(X) base a

• log(3X) base a

• log(3) base a - log(X) base a

• log(3) base a * log(X) base a

How does the quotient law affect log(X/5) base a?

• log(X) base a + log(5) base a

• log(X) base a - log(5) base a

• log(5) base a - log(X) base a

• log(X/5) base a

What is the simplified form of log(Y^5) base a using the power law?

• log(5Y) base a

• log(Y^5) base a

• log(Y) base a / 5

• 5 * log(Y) base a

How can you express log(XY) base a using the product law?

• log(X) base a - log(Y) base a

• log(X) base a + log(Y) base a

• log(XY) base a

• log(X) base a * log(Y) base a

What is the result of combining log(X) base a and log(Y^2) base a?

• log(X/Y^2) base a

• log(X) base a - log(Y^2) base a

• log(X) base a + log(Y^2) base a

• log(XY^2) base a

How can you express log(X) base a + log(Y) base a - 1 as a single logarithm?

• log(XY/a) base a

• log(XY) base a

• log(X/Y) base a

• log(XY^2) base a

What is the simplified form of 2 * log(X) base a using the power law?

• log(X^2) base a

• 2 * log(X) base a

• log(2X) base a

• log(X) base a / 2

How can you express 1/2 * log(Y) base a using the power law?

• log(Y^1/2) base a

• log(Y^2) base a

• 2 * log(Y) base a

• log(Y) base a / 2

What is the result of combining log(1/3) base a and 3 * log(3/4) base a?

• log((1/3)^3 * (3/4)^2) base a

• log(1/3) base a - 3 * log(3/4) base a

• log(1/3) base a + 3 * log(3/4) base a

• log((1/3)^2 * (3/4)^3) base a

How do you express log(X^2) base a - log(a^2) base a + log(Y^1/2) base a as a single logarithm?

• log((X^2 * Y^1/2) / a^2) base a

• log(X^2) base a - log(a^2) base a + log(Y^1/2) base a

• log((X^2 / Y^1/2) * a^2) base a

• log((X^2 * a^2) / Y^1/2) base a