Converting Logarithms to Exponential Form

Front

What is the definition of a logarithm?

Back

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

Front

How do you convert a logarithmic equation to exponential form?

Back

To convert a logarithmic equation log_b(a) = c to exponential form, rewrite it as b^c = a.

Front

What is the base in a logarithmic expression?

Back

The base in a logarithmic expression log_b(a) is the number b that is raised to the power of c to obtain a.

Front

What is the relationship between logarithms and exponents?

Back

Logarithms and exponents are inverse operations. If b^c = a, then log_b(a) = c.

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.

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What is the natural logarithm?

Back

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

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What is the common logarithm?

Back

The common logarithm is the logarithm to the base 10, denoted as log(x). It is often used in scientific calculations.

Front

How do you express an exponential equation in logarithmic form?

Back

To express an exponential equation b^c = a in logarithmic form, rewrite it as log_b(a) = c.

Front

What is the product rule for logarithms?

Back

The product rule states that log_b(xy) = log_b(x) + log_b(y) for any positive x and y.

Front

What is the quotient rule for logarithms?

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The quotient rule states that log_b(x/y) = log_b(x) - log_b(y) for any positive x and y.