Question

Solve this equation for x. Round your answer to the nearest hundredth.
1 = In(x + 7) ​

Answer 1

e^1 = x+7

e - 7 = x

x = -4.28

Answer 2

`\displaystyle x \approx -4.28`

General Formulas and Concepts:

Pre-Algebra

• Equality Properties

Algebra II

• Natural logarithms ln and Euler's number e

Explanation:

Step 1: Define

Identify

`\displaystyle 1 = ln(x + 7)`

Step 2: Solve for x

1. [Equality Property] e both sides:
   `\displaystyle e^1 = e^(ln(x + 7))`
2. Simplify:
   `\displaystyle x + 7 = e`
3. [Equality Property] Isolate x:
   `\displaystyle x = e - 7`
4. Evaluate:
   `\displaystyle x = -4.28172`