Precalculus Examples

$\log_{4} (5) - \log_{4} (\frac{5}{11})$

Step 1

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{4} (\frac{5}{\frac{5}{11}})$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\log_{4} (5 (\frac{11}{5}))$

Step 3

Cancel the common factor of $5$ .

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Step 3.1

Cancel the common factor.

$\log_{4} (5 (\frac{11}{5}))$

Step 3.2

Rewrite the expression.

$\log_{4} (11)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log_{4} (11)$

Decimal Form:

$1.72971580 \dots$