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- Equation:
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Equation log2(x^2+3x)=2
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Identical expressions
- log two (x^ two +3x)=2
- logarithm of 2(x squared plus 3x) equally 2
- logarithm of two (x to the power of two plus 3x) equally 2
- log2(x2+3x)=2
- log2x2+3x=2
- log2(x²+3x)=2
- log2(x to the power of 2+3x)=2
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Similar expressions
- log2(x^2-3x)=2
log2(x^2+3x)=2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/ 2 \
log\x + 3*x/
------------- = 2
log(2)
$$\frac{\log{\left(x^{2} + 3 x \right)}}{\log{\left(2 \right)}} = 2$$
Detail solution
Given the equation
$$\frac{\log{\left(x^{2} + 3 x \right)}}{\log{\left(2 \right)}} = 2$$
transform
$$\frac{\log{\left(\frac{x \left(x + 3\right)}{4} \right)}}{\log{\left(2 \right)}} = 0$$
$$\frac{\log{\left(x^{2} + 3 x \right)}}{\log{\left(2 \right)}} - 2 = 0$$
Do replacement
$$w = \log{\left(x^{2} + 3 x \right)}$$
Expand brackets in the left part
Move free summands (without w)
from left part to right part, we given:
$$\frac{w}{\log{\left(2 \right)}} = 2$$
Divide both parts of the equation by 1/log(2)
We get the answer: w = log(4)
do backward replacement
$$\log{\left(x^{2} + 3 x \right)} = w$$
substitute w:
$$\frac{\log{\left(x^{2} + 3 x \right)}}{\log{\left(2 \right)}} = 2$$
transform
$$\frac{\log{\left(\frac{x \left(x + 3\right)}{4} \right)}}{\log{\left(2 \right)}} = 0$$
$$\frac{\log{\left(x^{2} + 3 x \right)}}{\log{\left(2 \right)}} - 2 = 0$$
Do replacement
$$w = \log{\left(x^{2} + 3 x \right)}$$
Expand brackets in the left part
-2 + w/log2 = 0
Move free summands (without w)
from left part to right part, we given:
$$\frac{w}{\log{\left(2 \right)}} = 2$$
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
$$\log{\left(x^{2} + 3 x \right)} = w$$
substitute w:
Sum and product of roots
[src]
sum
0 - 4 + 1
$$\left(-4 + 0\right) + 1$$
=
-3
$$-3$$
product
1*-4*1
$$1 \left(-4\right) 1$$
=
-4
$$-4$$
-4
The graph