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3^x=7

3^x=7 equation

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Numerical solution:

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The solution

You have entered [src] 
 x    
3  = 7
3x=73^{x} = 7
Simplify
Detail solution
Given the equation:
3x=73^{x} = 7
or
3x−7=03^{x} - 7 = 0
or
3x=73^{x} = 7
or
3x=73^{x} = 7
- this is the simplest exponential equation
Do replacement
v=3xv = 3^{x}
we get
v−7=0v - 7 = 0
or
v−7=0v - 7 = 0
Move free summands (without v)
from left part to right part, we given:
v=7v = 7
We get the answer: v = 7
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⁡(7)log⁡(3)=log⁡(7)log⁡(3)x_{1} = \frac{\log{\left(7 \right)}}{\log{\left(3 \right)}} = \frac{\log{\left(7 \right)}}{\log{\left(3 \right)}}
The graph
-10.0-7.5-5.0-2.50.02.55.07.510.012.515.017.50500000
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
     log(7)
x1 = ------
     log(3)
x1=log⁡(7)log⁡(3)x_{1} = \frac{\log{\left(7 \right)}}{\log{\left(3 \right)}} 
x1 = log(7)/log(3)
Sum and product of roots [src] 
sum
log(7)
------
log(3)
log⁡(7)log⁡(3)\frac{\log{\left(7 \right)}}{\log{\left(3 \right)}} 
=
log(7)
------
log(3)
log⁡(7)log⁡(3)\frac{\log{\left(7 \right)}}{\log{\left(3 \right)}} 
product
log(7)
------
log(3)
log⁡(7)log⁡(3)\frac{\log{\left(7 \right)}}{\log{\left(3 \right)}} 
=
log(7)
------
log(3)
log⁡(7)log⁡(3)\frac{\log{\left(7 \right)}}{\log{\left(3 \right)}} 
log(7)/log(3)
Numerical answer [src] 
x1 = 1.77124374916142
x1 = 1.77124374916142
The graph
3^x=7 equation
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