Question

11

Select the correct answer.
Which expression is equivalent to the given expression?
In(2e/x)
O A. In 2 – In x
OB. 1 + In 2 - In x
Oc. In 2 + In x
OD. In 1 + In 2 - In
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Answer 1

B. 1 + ln 2 - ln x

General Formulas and Concepts:

Algebra II

• Natural logarithms ln and Euler's number e
• Logarithmic Property [Multiplying]:
  `\displaystyle log(ab) = log(a) + log(b)`
• Logarithmic Property [Dividing]:
  `\displaystyle log((a)/(b)) = log(a) - log(b)`

Explanation:

Step 1: Define

Identify

`\displaystyle ln((2e)/(x))`

Step 2: Simplify

1. Expand [Logarithmic Property - Dividing]:
   `\displaystyle ln((2e)/(x)) = ln(2e) - ln(x)`
2. Expand [Logarithmic Property - Multiplying]:
   `\displaystyle ln((2e)/(x)) = ln(2) + ln(e) - ln(x)`
3. Simplify:
   `\displaystyle ln((2e)/(x)) = ln(2) + 1 - ln(x)`
4. Rewrite:
   `\displaystyle ln((2e)/(x)) = 1 + ln(2) - ln(x)`