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Why is this concept useful?: Logarithms are the inverse of exponents. A natural log of a number is its logarithm to the base of the mathematical constant e, where e is an irrational number ~ 2.718. Natural log follows all the same properties of log.
Where does this concept fit into the curriculum?: High School

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How to use Natural Log:

\begin{array}{l} Solve\ for\ x\\ \\ 5^{x} =ln\left( 2e^{5}\right)\\ \\ First\ take\ the\ natural\ log\ of\ both\ sides\ to\ cancel\ the\ e\\ \ ln\left( 5^{x}\right) =ln\left( 2e^{5}\right)\\ \\ Then\ rewrite\ the\ expression\ to\ bring\ down\ the\ exponentsxln5=5\ ln\ ln( e) \ +ln⁡( 2)\\ As\ we\ know\ that\ ln\ ( e) \ =\ 1\ then\ xln( 5) =5+ln\ ln( 2)\\ \\ x=\frac{5+ln( 2)}{ln( 5)} \end{array}

Sample Math Problems

1. Rewrite as a single log expression:

2\ ln\ ln( x) -ln\ ln( x+1)

Solution:

2\ ln\ ln( x) -ln\ ln( x+1) \ =\ ln\left(\frac{x^{2}}{x+1}\right)

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Practice Math Problems

1.

Simplify\ 2e^{4lnln( 2e)}

2.

Evaluate\ 2e^{2} \times ln\ ln\left( e^{2}\right)

3.

Evaluate\ 6\ ln\ ln\left( e^{-3x}\right)

4.

Simplify\ 3\ ln\ ln\ \left( e^{7e}\right)

2. Solve for x

ln\ ln\left( e^{x}\right) \ +\ ln\ ln\left( e^{5}\right) =1

Solution:

\begin{array}{l} As\ ln\ ( e) \ =\ 1ln\ ln\left( e^{x}\right) \ +\ ln\ ln\left( e^{5}\right) \ =1\\ x+5=1,\ then\ x=\ -4 \end{array}

3. Rewrite the expression:

\left( e^{x^{2} -1}\right)

Solution:

\ 3\left( 3x^{2} -1\right) =3x^{2} -3

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Functions Worksheets

Natural Log

Related Topics

Normal Distribution

Tossing a Coin

Properties of Exponents

Solve for x

Math Tutoring to Boost Your Child’s Math Skills & Scores by 90% in Just 3 Months – Guaranteed!

Sample Math Problems

Download FREE Math Resources

8 Math Hacks and Tricks to Turn Your 'Okay' Math Student Into a Math Champion!

How to Make Sure Your Child is Highly Successful and Becomes a Millionaire

Practice Math Problems