Precalculus Examples

$\frac{2 \log (x)}{12} - \frac{\log (100)}{2}$

Step 1

Cancel the common factor of $2$ and $12$ .

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Step 1.1

Factor $2$ out of $2 \log (x)$ .

$\frac{2 (\log (x))}{12} - \frac{\log (100)}{2}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $12$ .

$\frac{2 \log (x)}{2 \cdot 6} - \frac{\log (100)}{2}$

Step 1.2.2

Cancel the common factor.

$\frac{2 \log (x)}{2 \cdot 6} - \frac{\log (100)}{2}$

Step 1.2.3

Rewrite the expression.

$\frac{\log (x)}{6} - \frac{\log (100)}{2}$

Step 2

Rewrite $\frac{\log (x)}{6}$ as $\frac{1}{6} \log (x)$ .

$\frac{1}{6} \log (x) - \frac{\log (100)}{2}$

Step 3

Simplify $\frac{1}{6} \log (x)$ by moving $\frac{1}{6}$ inside the logarithm.

$\log (x^{\frac{1}{6}}) - \frac{\log (100)}{2}$

Step 4

Rewrite $\frac{\log (100)}{2}$ as $\frac{1}{2} \log (100)$ .

$\log (x^{\frac{1}{6}}) - (\frac{1}{2} \log (100))$

Step 5

Simplify $\frac{1}{2} \log (100)$ by moving $\frac{1}{2}$ inside the logarithm.

$\log (x^{\frac{1}{6}}) - \log (100^{\frac{1}{2}})$

Step 6

Rewrite $100$ as $10^{2}$ .

$\log (x^{\frac{1}{6}}) - \log ({(10^{2})}^{\frac{1}{2}})$

Step 7

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\log (x^{\frac{1}{6}}) - \log (10^{2 (\frac{1}{2})})$

Step 8

Cancel the common factor of $2$ .

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Step 8.1

Cancel the common factor.

$\log (x^{\frac{1}{6}}) - \log (10^{2 (\frac{1}{2})})$

Step 8.2

Rewrite the expression.

$\log (x^{\frac{1}{6}}) - \log (10^{1})$

Step 9

Evaluate the exponent.

$\log (x^{\frac{1}{6}}) - \log (10)$

Step 10

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

$\log (x^{\frac{1}{6}}) - 1 \cdot 1$

Step 11

Multiply $- 1$ by $1$ .

$\log (x^{\frac{1}{6}}) - 1$