Set the argument of the logarithm equal to zero.

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

Subtract <math><mstyle displaystyle="true"><mn>12</mn></mstyle></math> from both sides of the equation.

Multiply each term in <math><mstyle displaystyle="true"><mo>-</mo><mi>x</mi><mo>=</mo><mo>-</mo><mn>12</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math>

Multiply each term in <math><mstyle displaystyle="true"><mo>-</mo><mi>x</mi><mo>=</mo><mo>-</mo><mn>12</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mrow><mo>(</mo><mo>-</mo><mi>x</mi><mo>)</mo></mrow><mo>⋅</mo><mo>-</mo><mn>1</mn></mstyle></math> .

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

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

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>12</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

The vertical asymptote occurs at <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mn>12</mn></mstyle></math> .

Vertical Asymptote: <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mn>12</mn></mstyle></math>

Vertical Asymptote: <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mn>12</mn></mstyle></math>

Replace the variable <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>11</mn></mstyle></math> in the expression.

Simplify the result.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>11</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>11</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>12</mn></mstyle></math> .

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> .

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.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>12</mn></mstyle></math> .

The final answer is <math><mstyle displaystyle="true"><mi>log</mi><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></mstyle></math> .

Convert <math><mstyle displaystyle="true"><mi>log</mi><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></mstyle></math> to decimal.

Replace the variable <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> in the expression.

Simplify the result.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>12</mn></mstyle></math> .

The final answer is <math><mstyle displaystyle="true"><mi>log</mi><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mstyle></math> .

Convert <math><mstyle displaystyle="true"><mi>log</mi><mrow><mo>(</mo><mn>3</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>12</mn></mstyle></math> and the points <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>11</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mn>10</mn><mo>,</mo><mn>0.30102999</mn><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mn>9</mn><mo>,</mo><mn>0.47712125</mn><mo>)</mo></mrow></mstyle></math> .

Vertical Asymptote: <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mn>12</mn></mstyle></math>

Do you know how to Graph f(x) = log of 12-x? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name | one billion three hundred four million six hundred forty-nine thousand six hundred thirty-three |
---|

- 1304649633 has 8 divisors, whose sum is
**1988037568** - The reverse of 1304649633 is
**3369464031** - Previous prime number is
**7**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 39
- Digital Root 3

Name | one billion three hundred five million two hundred ninety-one thousand one hundred ninety-four |
---|

- 1305291194 has 8 divisors, whose sum is
**1958305440** - The reverse of 1305291194 is
**4911925031** - Previous prime number is
**5563**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 35
- Digital Root 8

Name | two hundred sixty-five million six hundred thirty-seven thousand nine hundred forty-five |
---|

- 265637945 has 8 divisors, whose sum is
**320905800** - The reverse of 265637945 is
**549736562** - Previous prime number is
**149**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 47
- Digital Root 2