How to Solve Natural Logarithms? (+FREE Worksheet!)

A natural logarithm is a logarithm with base e, written ln. Solving equations with them relies on the fact that e to the power of ln x returns x, which is what lets you undo an exponential.

Examples

Natural Logarithms, Example 1:

Natural Logarithms, Example 2:

Natural Logarithms, Example 3:

Natural Logarithms, Example 4:

Exercises for Natural Logarithms

Find the value of (x) in each equation.

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

1. (color{blue}{ln⁡(3)})
2. (color{blue}{frac{e+1}{3}})
3. (color{blue}{e^9})
4. (color{blue}{2ln(3)})
5. (color{blue}{e^{e^2}})
6. (color{blue}{frac{e-4}{2}})

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