Simplify/Condense log of 25x^3+3 log of 1/x

$\log (25 x^{3}) + 3 \log (\frac{1}{x})$

Step 1

Simplify each term.

Simplify $3 \log (\frac{1}{x})$ by moving $3$ inside the logarithm.

$\log (25 x^{3}) + \log ({(\frac{1}{x})}^{3})$

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

$\log (25 x^{3}) + \log (\frac{1^{3}}{x^{3}})$

One to any power is one.

$\log (25 x^{3}) + \log (\frac{1}{x^{3}})$

Step 2

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

$\log (25 x^{3} \frac{1}{x^{3}})$

Step 3

Cancel the common factor of $x^{3}$ .

Factor $x^{3}$ out of $25 x^{3}$ .

$\log (x^{3} \cdot 25 \frac{1}{x^{3}})$

Cancel the common factor.

$\log (x^{3} \cdot 25 \frac{1}{x^{3}})$

Rewrite the expression.

$\log (25)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log (25)$

Decimal Form:

$1.39794000 \dots$