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-Answers and Explanations
- What is the Best Laptop for College Students?
- How to Understand Decimals Conveyed in Words
- Completing a Table and Make a Graph of Ratios and Rates
- How to Use Memory Tricks to Memorize Math Formulas?
- 4th Grade Ohio’s State Tests Math Worksheets: FREE & Printable
- Accuplacer Math Formulas
- The Ultimate ISEE Upper Level Math Formula Cheat Sheet
- 8th Grade IAR Math Worksheets: FREE & Printable
- The Ultimate 7th Grade North Carolina EOG Math Course (+FREE Worksheets)
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.