Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

Multiply $4$ by $1$ .

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Move $- 1$ to the left of $\log (4)$ .

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

Step 1.4

Rewrite $- 1 \log (4)$ as $- \log (4)$ .

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

Step 1.5

Multiply $4$ by $1$ .

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

Step 1.6

Combine $\frac{1}{x}$ and $\log (4)$ .

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

Step 1.7

Multiply $4$ by $1$ .

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

Step 2

Subtract $\log (4)$ from $- \log (4)$ .

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

Step 3

Simplify each term.

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Step 3.1

Simplify $- 2 \log (4)$ by moving $2$ inside the logarithm.

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

Step 3.2

Raise $4$ to the power of $2$ .

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

Step 4

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

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