Mister Exam

Other calculators


log2(x^2+3x)=2

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

The teacher will be very surprised to see your correct solution 😉

v

Numerical solution:

Do search numerical solution at [, ]

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
-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:
The graph
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
Rapid solution [src]
x1 = -4
$$x_{1} = -4$$
x2 = 1
$$x_{2} = 1$$
Numerical answer [src]
x1 = -4.0
x2 = 1.0
x2 = 1.0
The graph
log2(x^2+3x)=2 equation