Solving Logarithmic Equations

Front

What is a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number. For example, if b^y = x, then log_b(x) = y.

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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.

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What is the natural logarithm?

Back

The natural logarithm, denoted as ln(x), is the logarithm to the base e, where e is approximately equal to 2.71828.

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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.

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What is the product rule for 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 for 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 for logarithms?

Back

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

Front

How do you solve logarithmic equations with the same base?

Back

If log_b(A) = log_b(B), then A = B.

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 (0, ∞), meaning it only accepts positive real numbers.