Solving Equations with Logarithms

Front

What is a logarithm?

Back

A logarithm is the power to which a number (the base) must be raised to obtain another number. For example, log_b(a) = c means b^c = a.

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What is the base of a logarithm?

Back

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

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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

What is the product rule of logarithms?

Back

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

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What is the quotient rule of logarithms?

Back

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

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What is the power rule of logarithms?

Back

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

Front

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

Back

To solve log_b(x) = c, rewrite it in exponential form: x = b^c.

Front

What is the definition of a logarithmic function?

Back

A logarithmic function is the inverse of an exponential function, typically written as f(x) = log_b(x).

Front

What is the domain of a logarithmic function?

Back

The domain of a logarithmic function is all positive real numbers (x > 0).

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What is the range of a logarithmic function?

Back

The range of a logarithmic function is all real numbers.