Logarithms & Exponential Functions Test

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 of logarithms?

Back

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

Front

What is the quotient rule of logarithms?

Back

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

Front

What is the power rule of logarithms?

Back

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

Front

How do you convert a logarithmic equation to exponential form?

Back

To convert log_b(a) = c to exponential form, rewrite it as b^c = a.

Front

What is the value of log_4(16)?

Back

2, because 4^2 = 16.

Front

What is the formula for compound interest?

Back

A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the rate, n is the number of times interest is compounded per year, and t is the number of years.

Front

What is the y-intercept of the function f(x) = 6(2.5)^x?

Back

6, because when x = 0, f(0) = 6(2.5)^0 = 6.

Front

What is the definition of an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is the base, and x is the exponent.