Solving Exponential and Logarithmic Equations Flashcard

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

How do you convert a logarithmic equation to an exponential form?

Back

To convert log_b(a) = c to exponential form, use the formula b^c = a.

Front

What is the product rule of logarithms?

Back

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

Front

What is the quotient rule of logarithms?

Back

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

Front

What is the power rule of logarithms?

Back

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

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

How do you solve the equation log_b(x) = c?

Back

To solve log_b(x) = c, convert to exponential form: x = b^c.

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

How do you solve an exponential equation of the form a^x = b?

Back

To solve a^x = b, take the logarithm of both sides: x = log_a(b).

Front

What is the natural logarithm?

Back

The natural logarithm, denoted as ln(x), is the logarithm to the base e, where e is approximately 2.718.