Question

Solve this equation for x. Round your answer to the nearest hundredth.
8 = In(x + 3) ​

Answer 1

`\displaystyle x = 2977.96`

General Formulas and Concepts:

Pre-Algebra

• Equality Properties

Algebra II

• Natural logarithms ln and Euler's number e

Explanation:

Step 1: Define

Identify

`\displaystyle 8 = ln(x + 3)`

Step 2: Solve for x

1. [Equality Properties] e both sides:
   `\displaystyle e^8 = e^(ln(x + 3))`
2. Simplify:
   `\displaystyle x + 3 = e^8`
3. [Equality Property] Subtract 3 on both sides:
   `\displaystyle x = e^8 - 3`
4. Evaluate:
   `\displaystyle x = 2977.96`

Answer 2

2977.96 =x

Explanation:

8 = In(x + 3) ​

Raise each side to the base of e

e^8 = e^ ln(x+3)

e^8 = x+3

Subtract 3 from each side

e^8 -3 = x+3-3

e^8 -3= x

2977.95798 = x

Rounding to the nearest hundredth

2977.96 =x