Algebra Examples

$\log_{7} (3 x^{3} + x) - \log_{7} (x) = 2$

Step 1

Subtract $2$ from both sides of the equation.

$\log_{7} (3 x^{3} + x) - \log_{7} (x) - 2 = 0$

Step 2

Simplify $\log_{7} (3 x^{3} + x) - \log_{7} (x) - 2$ .

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Step 2.1

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{7} (\frac{3 x^{3} + x}{x}) - 2 = 0$

Step 2.2

Simplify each term.

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Step 2.2.1

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

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Step 2.2.1.1

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

$\log_{7} (\frac{x (3 x^{2}) + x}{x}) - 2 = 0$

Step 2.2.1.2

Raise $x$ to the power of $1$ .

$\log_{7} (\frac{x (3 x^{2}) + x^{1}}{x}) - 2 = 0$

Step 2.2.1.3

Factor $x$ out of $x^{1}$ .

$\log_{7} (\frac{x (3 x^{2}) + x \cdot 1}{x}) - 2 = 0$

Step 2.2.1.4

Factor $x$ out of $x (3 x^{2}) + x \cdot 1$ .

$\log_{7} (\frac{x (3 x^{2} + 1)}{x}) - 2 = 0$

Step 2.2.2

Cancel the common factor of $x$ .

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Step 2.2.2.1

Cancel the common factor.

$\log_{7} (\frac{x (3 x^{2} + 1)}{x}) - 2 = 0$

Step 2.2.2.2

Divide $3 x^{2} + 1$ by $1$ .

$\log_{7} (3 x^{2} + 1) - 2 = 0$

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.