Solving Exponential & 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, 2^x = 8.

Front

How do you solve the equation 2^x = 16?

Back

x = 4, because 2^4 = 16.

Front

What is a logarithmic equation?

Back

A logarithmic equation is an equation that involves a logarithm of a variable. For example, log(x) = 3.

Front

How do you solve the equation log(x) = 2?

Back

x = 100, because 10^2 = 100.

Front

What is the change of base formula for logarithms?

Back

The change of base formula is log_b(a) = log_k(a) / log_k(b), where k is any positive number.

Front

What is the product property of logarithms?

Back

The product property states that log_b(mn) = log_b(m) + log_b(n).

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What is the quotient property of logarithms?

Back

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

Front

What is the power property of logarithms?

Back

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

Front

How do you solve the equation log_2(8) = x?

Back

x = 3, because 2^3 = 8.

Front

What is the definition of a logarithm?

Back

A logarithm is the inverse operation to exponentiation, answering the question: to what exponent must a base be raised to produce a given number?