Precalculus Examples

$\frac{1}{5 \log_{4} (6 x)} - \log_{4} (y)$

Step 1

Simplify each term.

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Step 1.1

Simplify $5 \log_{4} (6 x)$ by moving $5$ inside the logarithm.

$\frac{1}{\log_{4} ({(6 x)}^{5})} - \log_{4} (y)$

Step 1.2

Simplify the denominator.

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Step 1.2.1

Apply the product rule to $6 x$ .

$\frac{1}{\log_{4} (6^{5} x^{5})} - \log_{4} (y)$

Step 1.2.2

Raise $6$ to the power of $5$ .

$\frac{1}{\log_{4} (7776 x^{5})} - \log_{4} (y)$

Step 2

To write $- \log_{4} (y)$ as a fraction with a common denominator, multiply by $\frac{\log_{4} (7776 x^{5})}{\log_{4} (7776 x^{5})}$ .

$\frac{1}{\log_{4} (7776 x^{5})} - \log_{4} (y) \cdot \frac{\log_{4} (7776 x^{5})}{\log_{4} (7776 x^{5})}$

Step 3

Combine $- \log_{4} (y)$ and $\frac{\log_{4} (7776 x^{5})}{\log_{4} (7776 x^{5})}$ .

$\frac{1}{\log_{4} (7776 x^{5})} + \frac{- \log_{4} (y) \log_{4} (7776 x^{5})}{\log_{4} (7776 x^{5})}$

Step 4

Combine the numerators over the common denominator.

$\frac{1 - \log_{4} (y) \log_{4} (7776 x^{5})}{\log_{4} (7776 x^{5})}$