1Cademy - Try It 10.62: Applying the Quotient Property of Logarithms

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Logarithmic Function

Example

Try It 10.62: Applying the Quotient Property of Logarithms

Apply the Quotient Property of Logarithms, $\log_a \frac{M}{N} = \log_a M - \log_a N$ , to expand and simplify logarithmic expressions.

For the expression $\log_2 \frac{5}{4}$ , applying the property results in $\log_2 5 - \log_2 4$ . Since $2^2 = 4$ , $\log_2 4$ evaluates to $2$ . The expression simplifies to $\log_2 5 - 2$ .

For the common logarithm $\log \frac{10}{y}$ , applying the property gives $\log 10 - \log y$ . Since the base is understood to be $10$ , $\log 10$ evaluates to $1$ . The final simplified expression is $1 - \log y$ .