Precalculus Examples

$\log (x) + \frac{1}{\log (x)}$

Step 1

To write $\log (x)$ as a fraction with a common denominator, multiply by $\frac{\log (x)}{\log (x)}$ .

$\frac{\log (x) \log (x)}{\log (x)} + \frac{1}{\log (x)}$

Step 2

Combine the numerators over the common denominator.

$\frac{\log (x) \log (x) + 1}{\log (x)}$

Step 3

Multiply $\log (x) \log (x)$ .

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Step 3.1

Raise $\log (x)$ to the power of $1$ .

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

Step 3.2

Raise $\log (x)$ to the power of $1$ .

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

Step 3.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 3.4

Add $1$ and $1$ .

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