Solving Logarithmic Equations: Find x in 9 ln(7-x) = 8

Solving the Logarithmic Equation 9 ln(7 - x) = 8

Let's break down how to solve the logarithmic equation 9 ln(7 - x) = 8, step-by-step:

Isolate the logarithm: Divide both sides of the equation by 9:
```
ln(7 - x) = 8/9
```
Exponentiate both sides: Use the base 'e' to exponentiate both sides:
```
e^(ln(7 - x)) = e^(8/9)
```
Simplify using logarithmic properties: Recall that e^(ln(x)) = x. Applying this simplifies the equation to:
```
7 - x = e^(8/9)
```
Isolate x: Subtract 7 from both sides:
```
-x = e^(8/9) - 7
```
Solve for x: Multiply both sides by -1:
```
x = -e^(8/9) + 7
```

Therefore, the solution to the logarithmic equation 9 ln(7 - x) = 8 is x = -e^(8/9) + 7.