Precalculus Examples

$\log (4 x) - \log (4) (x - 1) - \frac{1}{2}$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$\log (4 x) - \log (4) x - \log (4) \cdot - 1 - \frac{1}{2}$

Step 1.2

Multiply $- \log (4) \cdot - 1$ .

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Step 1.2.1

Multiply $- 1$ by $- 1$ .

$\log (4 x) - \log (4) x + 1 \log (4) - \frac{1}{2}$

Step 1.2.2

Multiply $\log (4)$ by $1$ .

$\log (4 x) - \log (4) x + \log (4) - \frac{1}{2}$

Step 2

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$- \log (4) x + \log (4 x \cdot 4) - \frac{1}{2}$

Step 3

Multiply $4$ by $4$ .

$- \log (4) x + \log (16 x) - \frac{1}{2}$

Step 4

Reorder factors in $- \log (4) x + \log (16 x) - \frac{1}{2}$ .

$- x \log (4) + \log (16 x) - \frac{1}{2}$