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 | three hundred five million thirty-two thousand six hundred sixty-seven |
---|

- 305032667 has 4 divisors, whose sum is
**308893920** - The reverse of 305032667 is
**766230503** - Previous prime number is
**79**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 32
- Digital Root 5

Name | five hundred seventy-four million three hundred twenty-eight thousand three hundred seventy-three |
---|

- 574328373 has 8 divisors, whose sum is
**766516608** - The reverse of 574328373 is
**373823475** - Previous prime number is
**1033**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 42
- Digital Root 6

Name | one billion eight hundred thirty-six million three hundred thirty-six thousand one hundred ninety-nine |
---|

- 1836336199 has 16 divisors, whose sum is
**1944518400** - The reverse of 1836336199 is
**9916336381** - Previous prime number is
**89**

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