Exponentials and Logarithms Review

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 a positive real number, and x is the exponent.

Front

What is the logarithmic form of the equation 2^3 = 8?

Back

log_2(8) = 3

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to obtain a given number. For example, in log_b(a) = c, b is the base.

Front

Evaluate log_10(100)

Back

2

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 value of log_b(b^x)?

Back

x

Front

Rewrite the equation 5^x = 25 in logarithmic form.

Back

log_5(25) = x

Front

What is the product rule for logarithms?

Back

The product rule states that log_b(m * n) = log_b(m) + log_b(n).

Front

What is the quotient rule for logarithms?

Back

The quotient rule states that log_b(m / n) = log_b(m) - log_b(n).

Front

What is the power rule for logarithms?

Back

The power rule states that log_b(m^p) = p * log_b(m).