Interchange the variables.

Rewrite the equation as <math><mstyle displaystyle="true"><mi>log</mi><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>8</mn><mo>)</mo></mrow><mo>=</mo><mi>x</mi></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mi>log</mi><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>8</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> <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> .

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

Rewrite the equation as <math><mstyle displaystyle="true"><mi>y</mi><mo>-</mo><mn>8</mn><mo>=</mo><msup><mrow><mn>10</mn></mrow><mrow><mi>x</mi></mrow></msup></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> to both sides of the equation.

Replace the <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> with <math><mstyle displaystyle="true"><msup><mrow><mi>f</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> to show the final answer.

Set up the composite result function.

Evaluate <math><mstyle displaystyle="true"><mi>g</mi><mrow><mo>(</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math> by substituting in the value of <math><mstyle displaystyle="true"><mi>f</mi></mstyle></math> into <math><mstyle displaystyle="true"><mi>g</mi></mstyle></math> .

Exponentiation and log are inverse functions.

Combine the opposite terms in <math><mstyle displaystyle="true"><mi>x</mi><mo>-</mo><mn>8</mn><mo>+</mo><mn>8</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mo>-</mo><mn>8</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Since <math><mstyle displaystyle="true"><mi>g</mi><mrow><mo>(</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>=</mo><mi>x</mi></mstyle></math> , <math><mstyle displaystyle="true"><msup><mrow><mi>f</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mn>10</mn></mrow><mrow><mi>x</mi></mrow></msup><mo>+</mo><mn>8</mn></mstyle></math> is the inverse of <math><mstyle displaystyle="true"><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mi>log</mi><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mn>8</mn><mo>)</mo></mrow></mstyle></math> .

Do you know how to Find the Inverse y = log of x-8? 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 | ninety-six million one hundred eighty-nine thousand eight |
---|

- 96189008 has 32 divisors, whose sum is
**486956934** - The reverse of 96189008 is
**80098169** - Previous prime number is
**2**

- Is Prime? no
- Number parity even
- Number length 8
- Sum of Digits 41
- Digital Root 5

Name | six hundred seventy-one million two hundred forty-seven thousand six hundred eighty-nine |
---|

- 671247689 has 4 divisors, whose sum is
**767140224** - The reverse of 671247689 is
**986742176** - Previous prime number is
**7**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 50
- Digital Root 5

Name | six hundred twenty-five million one hundred seventy-three thousand six hundred forty-nine |
---|

- 625173649 has 8 divisors, whose sum is
**627495080** - The reverse of 625173649 is
**946371526** - Previous prime number is
**541**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 43
- Digital Root 7