Log Properties & Graphing

Front

What is the property of logarithms that allows you to expand the expression 6log₈u - 2log₈v?

Back

Using the properties of logarithms, you can expand this expression as follows: 6log₈u - 2log₈v = log₈(u^6) - log₈(v^2) = log₈(\frac{u^6}{v^2}).

Front

What is the domain of the function f(x) = ln(-x) + 6?

Back

The domain of f(x) = ln(-x) + 6 is (-∞, 0) because the argument of the natural logarithm must be positive.

Front

What is the range of the function f(x) = ln(-x) + 6?

Back

The range of f(x) = ln(-x) + 6 is (-∞, ∞) because the natural logarithm can take any real number value.

Front

What transformations are represented in the equation f(x) = -e^(x+4) - 7?

Back

The transformations are: Left 4 (horizontal shift), Down 7 (vertical shift), and Reflection over the x-axis.

Front

Write the logarithmic form of the equation 8^3 = 512.

Back

The logarithmic form is log₈512 = 3.

Front

Write the exponential form of the equation log₃(1/27) = -3.

Back

The exponential form is 3^-3 = 1/27.

Front

What is the change of base formula for logarithms?

Back

The change of base formula states that log_b(a) = log_k(a) / log_k(b) for any positive k.

Front

What is the product property of logarithms?

Back

The product property states that log_b(xy) = log_b(x) + log_b(y).

Front

What is the quotient property of logarithms?

Back

The quotient property states that log_b(x/y) = log_b(x) - log_b(y).

Front

What is the power property of logarithms?

Back

The power property states that log_b(xⁿ) = n * log_b(x).