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log2(x^2+3x)=2

log2(x^2+3x)=2 equation

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Numerical solution:

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The solution

You have entered [src] 
   / 2      \    
log\x  + 3*x/    
------------- = 2
    log(2)
log⁡(x2+3x)log⁡(2)=2\frac{\log{\left(x^{2} + 3 x \right)}}{\log{\left(2 \right)}} = 2
Simplify
Detail solution
Given the equation
log⁡(x2+3x)log⁡(2)=2\frac{\log{\left(x^{2} + 3 x \right)}}{\log{\left(2 \right)}} = 2
transform
log⁡(x(x+3)4)log⁡(2)=0\frac{\log{\left(\frac{x \left(x + 3\right)}{4} \right)}}{\log{\left(2 \right)}} = 0
log⁡(x2+3x)log⁡(2)−2=0\frac{\log{\left(x^{2} + 3 x \right)}}{\log{\left(2 \right)}} - 2 = 0
Do replacement
w=log⁡(x2+3x)w = \log{\left(x^{2} + 3 x \right)}
Expand brackets in the left part
-2 + w/log2 = 0

Move free summands (without w)
from left part to right part, we given:
wlog⁡(2)=2\frac{w}{\log{\left(2 \right)}} = 2
Divide both parts of the equation by 1/log(2)
w = 2 / (1/log(2))

We get the answer: w = log(4)
do backward replacement
log⁡(x2+3x)=w\log{\left(x^{2} + 3 x \right)} = w
substitute w:
The graph
05-20-15-10-51015-2020
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
0 - 4 + 1
(−4+0)+1\left(-4 + 0\right) + 1 
=
-3
−3-3 
product
1*-4*1
1(−4)11 \left(-4\right) 1 
=
-4
−4-4 
-4
Rapid solution [src] 
x1 = -4
x1=−4x_{1} = -4
Simplify 
x2 = 1
x2=1x_{2} = 1
Simplify
Numerical answer [src] 
x1 = -4.0
x2 = 1.0
x2 = 1.0
The graph
log2(x^2+3x)=2 equation
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