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.

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 \(x\).
- \(\color{blue}{e^x=3}\)
- \(\color{blue}{e^x=4}\)
- \(\color{blue}{e^x=8}\)
- \(\color{blue}{ln x=6}\)
- \(\color{blue}{ln (ln x)=5}\)
- \(\color{blue}{e^x=9}\)
- \(\color{blue}{ln(2x+5)=4}\)
- \(\color{blue}{ln(2x-1)=1}\)

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
- Full-Length PSAT 10 Math Practice Test
- Top 10 Tips to Overcome ASVAB Math Anxiety
- Exploring Geometry Fundamentals: Study of Points, Lines, and Planes
- How to Unlock the Path to Success: “TExES Core Subjects Math for Beginners” In-Depth Solution Manual
- How to Solve Special Systems
- The Ultimate Algebra 1 Course (+FREE Worksheets)
- GED Math Practice Test Questions
- The Ultimate SSAT Upper-Level Math Course (+FREE Worksheets)
- How to Solve Word Problems of Elapsed Time
- How to Multiply and Divide in Scientific Notation? (+FREE Worksheet!)
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.