Graph f(x)=3 log of x

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Trigonometry

$f (x) = 3 \log (x)$

Find the asymptotes.

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Set the argument of the logarithm equal to zero.

$x^{3} = 0$

Solve for $x$ .

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Take the cube root of both sides of the equation to eliminate the exponent on the left side.

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

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

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

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

Pull terms out from under the radical, assuming real numbers.

$x = 0$

The vertical asymptote occurs at $x = 0$ .

Vertical Asymptote: $x = 0$

Find the point at $x = 1$ .

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Replace the variable $x$ with $1$ in the expression.

$f (1) = 3 \log (1)$

Simplify the result.

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Logarithm base $10$ of $1$ is $0$ .

$f (1) = 3 \cdot 0$

Multiply $3$ by $0$ .

$f (1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Find the point at $x = 10$ .

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Replace the variable $x$ with $10$ in the expression.

$f (10) = 3 \log (10)$

Simplify the result.

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Logarithm base $10$ of $10$ is $1$ .

$f (10) = 3 \cdot 1$

Multiply $3$ by $1$ .

$f (10) = 3$

The final answer is $3$ .

$3$

Convert $3$ to decimal.

$y = 3$

Find the point at $x = 2$ .

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Replace the variable $x$ with $2$ in the expression.

$f (2) = 3 \log (2)$

Simplify the result.

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Simplify $3 \log (2)$ by moving $3$ inside the logarithm.

$f (2) = \log (2^{3})$

Raise $2$ to the power of $3$ .

$f (2) = \log (8)$

The final answer is $\log (8)$ .

$\log (8)$

Convert $\log (8)$ to decimal.

$y = 0.90308998$

The log function can be graphed using the vertical asymptote at $x = 0$ and the points $(1, 0), (10, 3), (2, 0.90308998)$ .

Vertical Asymptote: $x = 0$

$\begin{array}{c} x & y \\ 1 & 0 \\ 2 & 0.903 \\ 10 & 3 \end{array}$

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