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log4*(5+x)=2 equation

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Numerical solution:

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The solution

You have entered [src] 
log(4)*(5 + x) = 2
(x+5)log⁡(4)=2\left(x + 5\right) \log{\left(4 \right)} = 2
Simplify
Detail solution
Given the equation:
log(4)*(5+x) = 2

Expand expressions:
10*log(2) + 2*x*log(2) = 2

Reducing, you get:
-2 + 10*log(2) + 2*x*log(2) = 0

Expand brackets in the left part
-2 + 10*log2 + 2*x*log2 = 0

Move free summands (without x)
from left part to right part, we given:
2xlog⁡(2)+10log⁡(2)=22 x \log{\left(2 \right)} + 10 \log{\left(2 \right)} = 2
Divide both parts of the equation by (10*log(2) + 2*x*log(2))/x
x = 2 / ((10*log(2) + 2*x*log(2))/x)

We get the answer: x = (1 - log(32))/log(2)
The graph
-20.0-17.5-15.0-12.5-10.0-7.5-5.0-2.50.02.55.07.5-5050
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
2 - log(1024)
-------------
    log(4)
2−log⁡(1024)log⁡(4)\frac{2 - \log{\left(1024 \right)}}{\log{\left(4 \right)}} 
=
2 - log(1024)
-------------
    log(4)
2−log⁡(1024)log⁡(4)\frac{2 - \log{\left(1024 \right)}}{\log{\left(4 \right)}} 
product
2 - log(1024)
-------------
    log(4)
2−log⁡(1024)log⁡(4)\frac{2 - \log{\left(1024 \right)}}{\log{\left(4 \right)}} 
=
2 - log(1024)
-------------
    log(4)
2−log⁡(1024)log⁡(4)\frac{2 - \log{\left(1024 \right)}}{\log{\left(4 \right)}} 
(2 - log(1024))/log(4)
Rapid solution [src] 
     2 - log(1024)
x1 = -------------
         log(4)
x1=2−log⁡(1024)log⁡(4)x_{1} = \frac{2 - \log{\left(1024 \right)}}{\log{\left(4 \right)}} 
x1 = (2 - log(1024))/log(4)
Numerical answer [src] 
x1 = -3.55730495911104
x1 = -3.55730495911104
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