How to Solve Natural Logarithms Problems? (+FREE Worksheet!)
In this blog post, you will learn more about Natural Logarithms and how to solve problems related to natural logarithms.
![How to Solve Natural Logarithms Problems? (+FREE Worksheet!)](https://www.effortlessmath.com/wp-content/uploads/2019/09/Natural-Logarithms-Cover-512x240.jpg)
Related Topics
Step by step guide to solve Natural Logarithms
- A natural logarithm is a logarithm that has a special base of the mathematical constant \(e\), which is an irrational number approximately equal to \(2.71\).
- The natural logarithm of \(x\) is generally written as ln \(x\), or \(\log_{e}{x}\).
Natural Logarithms – Example 1:
Solve the equation for \(x\): \(e^x=3\)
Solution:
If \(f(x)=g(x)\),then: \(ln(f(x))=ln(g(x))→ln(e^x)=ln(3) \)
Use log rule: \(\log_{a}{x^b}=b \log_{a}{x}\), then: \(ln(e^x)=x ln(e)→xln(e)=ln(3) \)
\(ln(e)=1\), then: \(x=ln(3) \)
Best Algebra Prep Resource
Natural Logarithms – Example 2:
Solve equation for \(x\): \(ln(2x-1)=1\)
Solution:
Use log rule: \(a=\log_{b}{b^a}\), then: \(1=ln(e^1 )=ln(e)→ln(2x-1)=ln(e)\)
When the logs have the same base: \(\log_{b}{f(x)}=\log_{b}{g(x)}\), then: \(f(x)=g(x)\)
then: \(ln(2x-1)=ln(e)\), then: \(2x-1=e→x=\frac{e+1}{2}\)
Natural Logarithms – Example 3:
Solve the equation for \(x\): \(e^x=5\)
Solution:
If \(f(x)=g(x)\),then: \(ln(f(x))=ln(g(x))→ln(e^x)=ln(5) \)
Use log rule: \(\log_{a}{x^b}=b \log_{a}{x}\), then: \(ln(e^x)=x ln(e)→xln(e)=ln(5) \)
\(ln(e)=1\), then: \(x=ln(5) \)
Natural Logarithms – Example 4:
Solve equation for \(x\): \(ln(5x-1)=1\)
Solution:
Use log rule: \(a=\log_{b}{b^a}\), then: \(1=ln(e^1 )=ln(e)→ln(5x-1)=ln(e)\)
When the logs have the same base: \(\log_{b}{f(x)}=\log_{b}{g(x)}\), then: \(f(x)=g(x)\)
then: \(ln(5x-1)=ln(e)\), then: \(5x-1=e→x=\frac{e+1}{5}\)
Exercises to practice Natural Logarithms
The Perfect Book to Ace the College Algebra Course
Solve each equation for \(x\).
- \(\color{blue}{e^x=3}\)
- \(\color{blue}{e^x=4}\)
- \(\color{blue}{e^x=8}\)
- \(\color{blue}{ln x=6}\)
- \(\color{blue}{ln (ln x)=5}\)
- \(\color{blue}{e^x=9}\)
- \(\color{blue}{ln(2x+5)=4}\)
- \(\color{blue}{ln(2x-1)=1}\)
![](https://www.effortlessmath.com/wp-content/uploads/2019/12/answers.png)
Answers
- \(\color{blue}{x=ln 3}\)
- \(\color{blue}{x=ln 4,x=2ln(2)}\)
- \(\color{blue}{x=ln 8,x=3ln(2)}\)
- \(\color{blue}{x=e^6}\)
- \(\color{blue}{x=e^{e^5}}\)
- \(\color{blue}{x=ln 9,x=2ln(3)}\)
- \(\color{blue}{x=\frac{e^4-5}{2}}\)
- \(\color{blue}{x=\frac{e+1}{2}}\)
The Best Books You Need to Ace Algebra
Related to This Article
More math articles
- The Math Game Show: How to Find Probability of Simple and Opposite Events
- How to Write Linear Equations From Y-Intercept and A Slope
- Geometry Puzzle – Challenge 72
- Intelligent Math Puzzle – Challenge 78
- TASC Math – Test Day Tips
- PSAT Math FREE Sample Practice Questions
- How to Solve Percent Problems? (+FREE Worksheet!)
- 5 Tips for Surviving a Statistics Course
- Sum and Difference of Trigonometric Functions Formulas
- 5th Grade WVGSA Math Worksheets: FREE & Printable
What people say about "How to Solve Natural Logarithms Problems? (+FREE Worksheet!) - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.