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3^x-3=81

3^x-3=81 equation

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Numerical solution:

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The solution

You have entered [src] 
 x         
3  - 3 = 81
3x−3=813^{x} - 3 = 81
Simplify
Detail solution
Given the equation:
3x−3=813^{x} - 3 = 81
or
(3x−3)−81=0\left(3^{x} - 3\right) - 81 = 0
or
3x=843^{x} = 84
or
3x=843^{x} = 84
- this is the simplest exponential equation
Do replacement
v=3xv = 3^{x}
we get
v−84=0v - 84 = 0
or
v−84=0v - 84 = 0
Move free summands (without v)
from left part to right part, we given:
v=84v = 84
We get the answer: v = 84
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⁡(84)log⁡(3)=log⁡(84)log⁡(3)x_{1} = \frac{\log{\left(84 \right)}}{\log{\left(3 \right)}} = \frac{\log{\left(84 \right)}}{\log{\left(3 \right)}}
The graph
-7.5-5.0-2.50.02.55.07.510.012.515.017.520.0-500000010000000
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
     log(84)
x1 = -------
      log(3)
x1=log⁡(84)log⁡(3)x_{1} = \frac{\log{\left(84 \right)}}{\log{\left(3 \right)}} 
x1 = log(84)/log(3)
Sum and product of roots [src] 
sum
log(84)
-------
 log(3)
log⁡(84)log⁡(3)\frac{\log{\left(84 \right)}}{\log{\left(3 \right)}} 
=
log(84)
-------
 log(3)
log⁡(84)log⁡(3)\frac{\log{\left(84 \right)}}{\log{\left(3 \right)}} 
product
log(84)
-------
 log(3)
log⁡(84)log⁡(3)\frac{\log{\left(84 \right)}}{\log{\left(3 \right)}} 
=
log(84)
-------
 log(3)
log⁡(84)log⁡(3)\frac{\log{\left(84 \right)}}{\log{\left(3 \right)}} 
log(84)/log(3)
Numerical answer [src] 
x1 = 4.03310325630434
x1 = 4.03310325630434
The graph
3^x-3=81 equation
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