Algebra Examples

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

Step 1

Simplify the right side.

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Step 1.1

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

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Step 1.1.1

Simplify $2 \log_{3} (x)$ by moving $2$ inside the logarithm.

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

Step 1.1.2

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

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

Step 2

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

$2 x^{2} = 2 x^{2}$

Step 3

Solve for $x$ .

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Step 3.1

Move all terms containing $x$ to the left side of the equation.

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Step 3.1.1

Subtract $2 x^{2}$ from both sides of the equation.

$2 x^{2} - 2 x^{2} = 0$

Step 3.1.2

Subtract $2 x^{2}$ from $2 x^{2}$ .

$0 = 0$

Step 3.2

Since $0 = 0$ , the equation will always be true.

Always true

Step 4

The result can be shown in multiple forms.

Always true

Interval Notation:

$(- \infty, \infty)$