1Cademy - Try It 10.61: Writing Logarithms as a Difference of Logarithms

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Logarithmic Function

Example

Try It 10.61: Writing Logarithms as a Difference of Logarithms

Apply the Quotient Property of Logarithms, $\log_a \frac{M}{N} = \log_a M - \log_a N$ , to write logarithmic expressions as a difference of logarithms.

For the expression $\log_4 \frac{3}{4}$ , applying the property gives $\log_4 3 - \log_4 4$ . Since $\log_4 4$ evaluates to $1$ , this simplifies to $\log_4 3 - 1$ .

For the common logarithm $\log \frac{x}{1000}$ , applying the property yields $\log x - \log 1000$ . Since the base is understood to be $10$ and $10^3 = 1000$ , $\log 1000$ evaluates to $3$ . This simplifies the expression to $\log x - 3$ .