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e^x=3

e^x=3 equation

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Numerical solution:

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The solution

You have entered [src] 
 x    
E  = 3
ex=3e^{x} = 3
Simplify
Detail solution
Given the equation:
ex=3e^{x} = 3
or
ex−3=0e^{x} - 3 = 0
or
ex=3e^{x} = 3
or
ex=3e^{x} = 3
- this is the simplest exponential equation
Do replacement
v=exv = e^{x}
we get
v−3=0v - 3 = 0
or
v−3=0v - 3 = 0
Move free summands (without v)
from left part to right part, we given:
v=3v = 3
We get the answer: v = 3
do backward replacement
ex=ve^{x} = v
or
x=log⁡(v)x = \log{\left(v \right)}
The final answer
x1=log⁡(3)log⁡(e)=log⁡(3)x_{1} = \frac{\log{\left(3 \right)}}{\log{\left(e \right)}} = \log{\left(3 \right)}
The graph
-12.5-10.0-7.5-5.0-2.50.02.55.07.510.012.515.00100000
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = log(3)
x1=log⁡(3)x_{1} = \log{\left(3 \right)} 
x1 = log(3)
Sum and product of roots [src] 
sum
log(3)
log⁡(3)\log{\left(3 \right)} 
=
log(3)
log⁡(3)\log{\left(3 \right)} 
product
log(3)
log⁡(3)\log{\left(3 \right)} 
=
log(3)
log⁡(3)\log{\left(3 \right)} 
log(3)
Numerical answer [src] 
x1 = 1.09861228866811
x1 = 1.09861228866811
The graph
e^x=3 equation
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