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, log_b(a) = c means b^c = a.

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.

Front

What is the natural logarithm?

Back

The natural logarithm, denoted as ln(x), is the logarithm to the base e, where e is approximately 2.718.

Front

What is the product property of logarithms?

Back

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

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What is the power property of logarithms?

Back

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

Front

How do you solve the equation 2log_5(7) = 3x + 1 log_5(49)?

Back

First, simplify log_5(49) to 2log_5(7). Then, set the equation to 0 to find x.

Front

What does log_b(b) equal?

Back

log_b(b) = 1, because b^1 = b.

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What does log_b(1) equal?

Back

log_b(1) = 0, because b^0 = 1.

Front

What is the definition of a logarithmic equation?

Back

A logarithmic equation is an equation that involves a logarithm with a variable in its argument.