Precalculus Examples

$\log (2) \cdot 5 + \log (2) (x^{2} - 1) - \log (2) (x - 1)$

Step 1

Simplify each term.

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Step 1.1

Multiply $\log (2) \cdot 5$ .

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Step 1.1.1

Reorder $\log (2)$ and $5$ .

$5 \cdot \log (2) + \log (2) (x^{2} - 1) - \log (2) (x - 1)$

Step 1.1.2

Simplify $5 \cdot \log (2)$ by moving $5$ inside the logarithm.

$\log (2^{5}) + \log (2) (x^{2} - 1) - \log (2) (x - 1)$

Step 1.2

Raise $2$ to the power of $5$ .

$\log (32) + \log (2) (x^{2} - 1) - \log (2) (x - 1)$

Step 1.3

Apply the distributive property.

$\log (32) + \log (2) x^{2} + \log (2) \cdot - 1 - \log (2) (x - 1)$

Step 1.4

Move $- 1$ to the left of $\log (2)$ .

$\log (32) + \log (2) x^{2} - 1 \cdot \log (2) - \log (2) (x - 1)$

Step 1.5

Rewrite $- 1 \log (2)$ as $- \log (2)$ .

$\log (32) + \log (2) x^{2} - \log (2) - \log (2) (x - 1)$

Step 1.6

Apply the distributive property.

$\log (32) + \log (2) x^{2} - \log (2) - \log (2) x - \log (2) \cdot - 1$

Step 1.7

Multiply $- \log (2) \cdot - 1$ .

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Step 1.7.1

Multiply $- 1$ by $- 1$ .

$\log (32) + \log (2) x^{2} - \log (2) - \log (2) x + 1 \log (2)$

Step 1.7.2

Multiply $\log (2)$ by $1$ .

$\log (32) + \log (2) x^{2} - \log (2) - \log (2) x + \log (2)$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $\log (32) + \log (2) x^{2} - \log (2) - \log (2) x + \log (2)$ .

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Step 2.1.1

Add $- \log (2)$ and $\log (2)$ .

$\log (32) + \log (2) x^{2} - \log (2) x + 0$

Step 2.1.2

Add $\log (32) + \log (2) x^{2} - \log (2) x$ and $0$ .

$\log (32) + \log (2) x^{2} - \log (2) x$

Step 2.2

Reorder factors in $\log (32) + \log (2) x^{2} - \log (2) x$ .

$\log (32) + x^{2} \log (2) - x \log (2)$