Logs and Radicals Review

Front

What is the definition of a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number. For example, log_b(a) = c means b^c = a.

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 rule for logarithms?

Back

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

Front

What is the quotient rule for logarithms?

Back

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

Front

What is the power rule for logarithms?

Back

The power rule states that log_b(x^k) = k * log_b(x).

Front

What is the value of log_b(b)?

Back

The value of log_b(b) is 1, since b^1 = b.

Front

What is the value of log_b(1)?

Back

The value of log_b(1) is 0, since b^0 = 1.

Front

How do you evaluate log_12(1)?

Back

log_12(1) = 0, because 12^0 = 1.

Front

What is the formula for the area of a triangle given two sides and the included angle?

Back

Area = 1/2 * a * b * sin(C), where a and b are the lengths of the sides and C is the included angle.

Front

What is the average rate of change of a function f(x) on the interval [a, b]?

Back

Average rate of change = (f(b) - f(a)) / (b - a).