Trigonometry Examples

$\log (x) \cdot 3 = y$

Step 1

Solve for $y$ .

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Step 1.1

Rewrite the equation as $y = \log (x) \cdot 3$ .

$y = \log (x) \cdot 3$

Step 1.2

Multiply $\log (x) \cdot 3$ .

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Step 1.2.1

Reorder $\log (x)$ and $3$ .

$y = 3 \cdot \log (x)$

Step 1.2.2

Simplify $3 \cdot \log (x)$ by moving $3$ inside the logarithm.

$y = \log (x^{3})$

Step 2

Set the argument in $\log (x^{3})$ less than or equal to $0$ to find where the expression is undefined.

$x^{3} \leq 0$

Step 3

Solve for $x$ .

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Step 3.1

Take the specified root of both sides of the inequality to eliminate the exponent on the left side.

$\sqrt[3]{x^{3}} \leq \sqrt[3]{0}$

Step 3.2

Simplify the equation.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Pull terms out from under the radical.

$x \leq \sqrt[3]{0}$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Simplify $\sqrt[3]{0}$ .

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Step 3.2.2.1.1

Rewrite $0$ as $0^{3}$ .

$x \leq \sqrt[3]{0^{3}}$

Step 3.2.2.1.2

Pull terms out from under the radical.

$x \leq 0$

Step 4

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$x \leq 0$

$(- \infty, 0]$

Step 5