Set the argument of the logarithm equal to zero.

Solve for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

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

Simplify <math><mstyle displaystyle="true"><mroot><mrow><mn>0</mn></mrow><mrow><mn>3</mn></mrow></mroot></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>0</mn></mrow><mrow><mn>3</mn></mrow></msup></mstyle></math> .

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

The vertical asymptote occurs at <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mn>0</mn></mstyle></math> .

Vertical Asymptote: <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mn>0</mn></mstyle></math>

Vertical Asymptote: <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mn>0</mn></mstyle></math>

Replace the variable <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> in the expression.

Simplify the result.

Logarithm base <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

The final answer is <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Convert <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> to decimal.

Replace the variable <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> in the expression.

Simplify the result.

Logarithm base <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> of <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

The final answer is <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Convert <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> to decimal.

Replace the variable <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> in the expression.

Simplify the result.

Simplify <math><mstyle displaystyle="true"><mn>3</mn><mi>log</mi><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></mstyle></math> by moving <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> inside the logarithm.

Raise <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

The final answer is <math><mstyle displaystyle="true"><mi>log</mi><mrow><mo>(</mo><mn>8</mn><mo>)</mo></mrow></mstyle></math> .

Convert <math><mstyle displaystyle="true"><mi>log</mi><mrow><mo>(</mo><mn>8</mn><mo>)</mo></mrow></mstyle></math> to decimal.

The log function can be graphed using the vertical asymptote at <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mn>0</mn></mstyle></math> and the points <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mn>10</mn><mo>,</mo><mn>3</mn><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>0.90308998</mn><mo>)</mo></mrow></mstyle></math> .

Vertical Asymptote: <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mn>0</mn></mstyle></math>

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