Simplify/Condense log of 16x^2+2 log of 1/x

$\log (16 x^{2}) + 2 \log (\frac{1}{x})$

Simplify each term.

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

$\log (16 x^{2}) + \log ({(\frac{1}{x})}^{2})$

Apply the product rule to $\frac{1}{x}$ .

$\log (16 x^{2}) + \log (\frac{1^{2}}{x^{2}})$

One to any power is one.

$\log (16 x^{2}) + \log (\frac{1}{x^{2}})$

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log (16 x^{2} \frac{1}{x^{2}})$

Cancel the common factor of $x^{2}$ .

Factor $x^{2}$ out of $16 x^{2}$ .

$\log (x^{2} \cdot 16 \frac{1}{x^{2}})$

Cancel the common factor.

$\log (x^{2} \cdot 16 \frac{1}{x^{2}})$

Rewrite the expression.

$\log (16)$

The result can be shown in multiple forms.

Exact Form:

$\log (16)$

Decimal Form:

$1.20411998 \dots$