PH: L3.4 Exponential and Logarithmic Equations

Front

What is 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 (a positive real number), and x is the exponent.

Front

What is a logarithm?

Back

A logarithm is the inverse operation to exponentiation, indicating the power to which a base must be raised to obtain a given number. For example, if b^y = x, then log_b(x) = y.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to produce a given number. Common bases include 10 (common logarithm) and e (natural logarithm).

Front

What is the relationship between exponential and logarithmic functions?

Back

Exponential functions and logarithmic functions are inverses of each other. If y = b^x, then x = log_b(y).

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, allowing conversion between different logarithmic bases.

Front

What is the natural logarithm?

Back

The natural logarithm is the logarithm to the base e, denoted as ln(x). It is commonly used in calculus and mathematical analysis.

Front

What is the product rule for logarithms?

Back

The product rule states that log_b(xy) = log_b(x) + log_b(y), allowing the simplification of the logarithm of a product.

Front

What is the quotient rule for logarithms?

Back

The quotient rule states that log_b(x/y) = log_b(x) - log_b(y), allowing the simplification of the logarithm of a quotient.

Front

What is the power rule for logarithms?

Back

The power rule states that log_b(x^k) = k * log_b(x), allowing the simplification of the logarithm of a power.

Front

How do you solve an exponential equation?

Back

To solve an exponential equation, you can take the logarithm of both sides, use properties of logarithms, and isolate the variable.