Set the argument of the logarithm equal to zero.

Add <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to both sides of the equation.

The vertical asymptote occurs at <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mn>2</mn></mstyle></math> .

Vertical Asymptote: <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mn>2</mn></mstyle></math>

Vertical Asymptote: <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mn>2</mn></mstyle></math>

Replace the variable <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> in the expression.

Simplify the result.

Subtract <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Logarithm base <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> is <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>4</mn></mstyle></math> in the expression.

Simplify the result.

Subtract <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Logarithm base <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

The final answer is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Convert <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> to decimal.

Replace the variable <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> in the expression.

Simplify the result.

Subtract <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> .

Logarithm base <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> of <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Rewrite as an equation.

Rewrite <math><mstyle displaystyle="true"><msub><mi>log</mi><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow><mo>=</mo><mi>x</mi></mstyle></math> in exponential form using the definition of a logarithm. If <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> and <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> are positive real numbers and <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> does not equal <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> , then <math><mstyle displaystyle="true"><msub><mi>log</mi><mrow><mi>b</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mi>y</mi></mstyle></math> is equivalent to <math><mstyle displaystyle="true"><msup><mrow><mi>b</mi></mrow><mrow><mi>y</mi></mrow></msup><mo>=</mo><mi>x</mi></mstyle></math> .

Create equivalent expressions in the equation that all have equal bases.

Since the bases are the same, the two expressions are only equal if the exponents are also equal.

The variable <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> is equal to <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

The final answer is <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Convert <math><mstyle displaystyle="true"><mn>2</mn></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>2</mn></mstyle></math> and the points <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>3</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mn>4</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mn>6</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></mstyle></math> .

Vertical Asymptote: <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mn>2</mn></mstyle></math>

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