Solving Exponential and Logarithmic Equations

Front

What is an exponential equation?

Back

An exponential equation is an equation in which a variable appears in the exponent. For example, in the equation 2^x = 8, x is the variable in the exponent.

Front

What is a logarithmic equation?

Back

A logarithmic equation is an equation that involves a logarithm of a variable. For example, log_b(x) = y means that b^y = x.

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, where k is not equal to 1.

Front

How do you combine logarithms with the same base?

Back

You can combine logarithms with the same base using the properties: log_b(m) + log_b(n) = log_b(m*n) and log_b(m) - log_b(n) = log_b(m/n).

Front

What is the product property of logarithms?

Back

The product property of logarithms states that the logarithm of a product is the sum of the logarithms: log_b(m*n) = log_b(m) + log_b(n).

Front

What is the quotient property of logarithms?

Back

The quotient property of logarithms states that the logarithm of a quotient is the difference of the logarithms: log_b(m/n) = log_b(m) - log_b(n).

Front

What is the power property of logarithms?

Back

The power property of logarithms states that the logarithm of a number raised to a power is the power times the logarithm of the number: log_b(m^k) = k * log_b(m).

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 to simplify, and then solve for the variable.

Front

How do you solve a logarithmic equation?

Back

To solve a logarithmic equation, you can exponentiate both sides to eliminate the logarithm, then solve the resulting equation for the variable.

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).

Tags

CCSS.HSF.BF.B.5