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

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Multiply <math><mstyle displaystyle="true"><mi>log</mi><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mn>2</mn><mo>)</mo></mrow></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mi>log</mi><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mn>2</mn><mo>)</mo></mrow><mo>=</mo><mo>-</mo><mn>4</mn></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> <math><mstyle displaystyle="true"><mo>≠</mo></mstyle></math> <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> .

Rewrite the expression using the negative exponent rule <math><mstyle displaystyle="true"><msup><mrow><mi>b</mi></mrow><mrow><mo>-</mo><mi>n</mi></mrow></msup><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mrow><mi>b</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></mfrac></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Rewrite the equation as <math><mstyle displaystyle="true"><mi>x</mi><mo>-</mo><mn>2</mn><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>10000</mn></mrow></mfrac></mstyle></math> .

Move all terms not containing <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> to the right side of the equation.

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

Simplify the right side of the equation.

To write <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>1</mn></mrow></mfrac></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>10000</mn></mrow><mrow><mn>10000</mn></mrow></mfrac></mstyle></math> .

Write each expression with a common denominator of <math><mstyle displaystyle="true"><mn>10000</mn></mstyle></math> , by multiplying each by an appropriate factor of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Combine.

Multiply <math><mstyle displaystyle="true"><mn>10000</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>10000</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>20000</mn></mstyle></math> .

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Mixed Number Form:

Do you know how to Solve for x 1/2* log of x-2=-2? 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 seven hundred fifty-two million two hundred eighty-nine thousand five hundred twenty-eight |
---|

- 1752289528 has 64 divisors, whose sum is
**6454764288** - The reverse of 1752289528 is
**8259822571** - Previous prime number is
**6803**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 49
- Digital Root 4

Name | seven hundred twenty-one million five hundred thirty-three thousand eight hundred forty-four |
---|

- 721533844 has 32 divisors, whose sum is
**1639033056** - The reverse of 721533844 is
**448335127** - Previous prime number is
**163**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 37
- Digital Root 1

Name | five hundred eleven million seven hundred forty-nine thousand nine hundred eighty-seven |
---|

- 511749987 has 8 divisors, whose sum is
**549196032** - The reverse of 511749987 is
**789947115** - Previous prime number is
**41**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 51
- Digital Root 6