Mister Exam
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How to use it?
- Equation:
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Equation sin(-x)=0
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Equation 3x-1=2x
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Equation x/2+x/3=10
- Equation 2*x=5-y
- Express {x} in terms of y where:
- -20*x-18*y=-13
- 13*x+7*y=0
- 2*x-3*y=16
- -6*x+13*y=16
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Identical expressions
- log(three)*(two *x+ one)= two
- logarithm of (3) multiply by (2 multiply by x plus 1) equally 2
- logarithm of (three) multiply by (two multiply by x plus one) equally two
- log(3)(2x+1)=2
- log32x+1=2
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Similar expressions
- log(3)*(2*x-1)=2
- log3(2x+1)=log3(4-x)
- log3(2x+1)=log3(x+2)
- log3(2^x+1)=5-x
log(3)*(2*x+1)=2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
Expand expressions:
Reducing, you get:
Expand brackets in the left part
Move free summands (without x)
from left part to right part, we given:
$$2 x \log{\left(3 \right)} + \log{\left(3 \right)} = 2$$
Divide both parts of the equation by (2*x*log(3) + log(3))/x
We get the answer: x = -1/2 + 1/log(3)
log(3)*(2*x+1) = 2
Expand expressions:
2*x*log(3) + log(3) = 2
Reducing, you get:
-2 + 2*x*log(3) + log(3) = 0
Expand brackets in the left part
-2 + 2*x*log3 + log3 = 0
Move free summands (without x)
from left part to right part, we given:
$$2 x \log{\left(3 \right)} + \log{\left(3 \right)} = 2$$
Divide both parts of the equation by (2*x*log(3) + log(3))/x
x = 2 / ((2*x*log(3) + log(3))/x)
We get the answer: x = -1/2 + 1/log(3)
Rapid solution
[src]
1 1
x1 = - - + ------
2 log(3)
$$x_{1} = - \frac{1}{2} + \frac{1}{\log{\left(3 \right)}}$$
x1 = -1/2 + 1/log(3)
Sum and product of roots
[src]
sum
1 1 - - + ------ 2 log(3)
$$- \frac{1}{2} + \frac{1}{\log{\left(3 \right)}}$$
=
1 1 - - + ------ 2 log(3)
$$- \frac{1}{2} + \frac{1}{\log{\left(3 \right)}}$$
product
1 1 - - + ------ 2 log(3)
$$- \frac{1}{2} + \frac{1}{\log{\left(3 \right)}}$$
=
1 1 - - + ------ 2 log(3)
$$- \frac{1}{2} + \frac{1}{\log{\left(3 \right)}}$$
-1/2 + 1/log(3)
The graph