Solving Logarithmic Equations

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What is a logarithm?

Back

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

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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 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 equation?

Back

A logarithmic equation is an equation that involves a logarithm of a variable or expression.

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How do you isolate a variable in a logarithmic equation?

Back

To isolate a variable, use properties of logarithms to combine or separate terms, then convert to exponential form.

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What is the domain of a logarithmic function?

Back

The domain of a logarithmic function is the set of positive real numbers, as the logarithm of zero or a negative number is undefined.

Front

What does it mean if log_b(a) = log_b(c)?

Back

If log_b(a) = log_b(c), then a = c, provided that b > 0 and b ≠ 1.