Final answer:
To solve the equation for x when y = 9, we exponentiate both sides with base e, subtract e from both sides, and finally divide by 9, which yields the solution x = (e^9 - e) / 9.
Step-by-step explanation:
To solve the equation In(9x + e) for x when y = 9, we use the definition of the logarithm to isolate x:
Let's solve the given equation for x when y = 9: Original equation: ln(9x + e) = y Given that y = 9, we can substitute 9 in for y: ln(9x + e) = 9 Now, we can solve for x by following these steps:
1. Exponentiate both sides of the equation to get rid of the natural logarithm. Recall that ln(a) = b is equivalent to e^b = a. e^(ln(9x + e)) = e^9 Since e^(ln(a)) is just a (because e and ln are inverse functions), we now have: 9x + e = e^9 2.
Subtract e from both sides to isolate the term with x: 9x = e^9 - e 3. Divide both sides by 9 to solve for x: x = (e^9 - e) / 9 And that's the solution for x when y = 9. If you wanted to get a numerical approximation for x, you would use the mathematical constant e ≈ 2.71828 to evaluate the expression (e^9 - e) / 9.
- Firstly, since In represents the natural logarithm, we can rewrite the equation as ey = 9x + e.
- Setting y = 9 in this equation gives us e9 = 9x + e.
- To solve for x, we subtract e from both sides to obtain 9x = e9 - e.
- Finally, we divide both sides by 9 to get x = (e9 - e) / 9.
Therefore, the value of x when y = 9 is (e9 - e) / 9.