Precalculus Examples

$\log (\frac{10 x}{x (x^{2} + 1) (x^{4} + 2)})$

Step 1

Rewrite $\log (\frac{10 x}{x (x^{2} + 1) (x^{4} + 2)})$ as $\log (10 x) - \log (x (x^{2} + 1) (x^{4} + 2))$ .

$\log (10 x) - \log (x (x^{2} + 1) (x^{4} + 2))$

Step 2

Rewrite $\log (10 x)$ as $\log (10) + \log (x)$ .

$\log (10) + \log (x) - \log (x (x^{2} + 1) (x^{4} + 2))$

Step 3

Logarithm base $10$ of $10$ is $1$ .

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

Step 4

Rewrite $\log (x (x^{2} + 1) (x^{4} + 2))$ as $\log (x (x^{2} + 1)) + \log (x^{4} + 2)$ .

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

Step 5

Rewrite $\log (x (x^{2} + 1))$ as $\log (x) + \log (x^{2} + 1)$ .

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

Step 6

Apply the distributive property.

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

Step 7

Subtract $\log (x)$ from $\log (x)$ .

$1 + 0 - \log (x^{2} + 1) - \log (x^{4} + 2)$

Step 8

Add $1$ and $0$ .

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