Question

Solve for X

Answer 1

Answer:

$x = \pm e^{-1}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Equality Properties

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtract Property of Equality

Algebra I

• Solving quadratics
• Multiple roots

Algebra II

• Logarithms
• Euler's number e

Step-by-step explanation:

Step 1: Define

$\displaystyle ln(x^2) = -2$

Step 2: Solve for x

1. Raise both sides by e:                    $e^{\displaystyle ln(x^2)} = e^{-2}$
2. Simplify equation:                           $x^2 = e^{-2}$
3. Square root both sides:                 $x = \pm e^{-1}$

Answer 2

Answer:

Step-by-step explanation:

lnx^n=nlnx

$\ln x^2=-2\\2\ln x=-2\\\\\ln x=-1\\\\x>0\\x=e^{-1}\\or~x=\frac{1}{e}$