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3^x=-1

3^x=-1 equation

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Numerical solution:

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The solution

You have entered [src] 
 x     
3  = -1
3x=−13^{x} = -1
Simplify
Detail solution
Given the equation:
3x=−13^{x} = -1
or
3x+1=03^{x} + 1 = 0
or
3x=−13^{x} = -1
or
3x=−13^{x} = -1
- this is the simplest exponential equation
Do replacement
v=3xv = 3^{x}
we get
v+1=0v + 1 = 0
or
v+1=0v + 1 = 0
Move free summands (without v)
from left part to right part, we given:
v=−1v = -1
We get the answer: v = -1
do backward replacement
3x=v3^{x} = v
or
x=log⁡(v)log⁡(3)x = \frac{\log{\left(v \right)}}{\log{\left(3 \right)}}
The final answer
x1=log⁡(−1)log⁡(3)=iπlog⁡(3)x_{1} = \frac{\log{\left(-1 \right)}}{\log{\left(3 \right)}} = \frac{i \pi}{\log{\left(3 \right)}}
The graph
024-14-12-10-8-6-4-2-5050
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
      pi*I 
x1 = ------
     log(3)
x1=iπlog⁡(3)x_{1} = \frac{i \pi}{\log{\left(3 \right)}} 
x1 = i*pi/log(3)
Sum and product of roots [src] 
sum
 pi*I 
------
log(3)
iπlog⁡(3)\frac{i \pi}{\log{\left(3 \right)}} 
=
 pi*I 
------
log(3)
iπlog⁡(3)\frac{i \pi}{\log{\left(3 \right)}} 
product
 pi*I 
------
log(3)
iπlog⁡(3)\frac{i \pi}{\log{\left(3 \right)}} 
=
 pi*I 
------
log(3)
iπlog⁡(3)\frac{i \pi}{\log{\left(3 \right)}} 
pi*i/log(3)
Numerical answer [src] 
x1 = 2.85960086738013*i
x1 = 2.85960086738013*i
The graph
3^x=-1 equation
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