Exponential and Logarithmic 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, if b^y = x, then log_b(x) = y.

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b), where k is any positive number.

Front

Convert the logarithmic equation log_2(8) = 3 to exponential form.

Back

2^3 = 8.

Front

What is the product rule for logarithms?

Back

log_b(xy) = log_b(x) + log_b(y).

Front

What is the quotient rule for logarithms?

Back

log_b(x/y) = log_b(x) - log_b(y).

Front

What is the power rule for logarithms?

Back

log_b(x^k) = k * log_b(x).

Front

Solve for x: log_5(x) = 2.

Back

x = 25.

Front

If log_10(1000) = x, what is the value of x?

Back

x = 3.

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.

Front

Convert the exponential equation 3^x = 81 to logarithmic form.

Back

log_3(81) = x.