Mister Exam
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- Equation:
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Equation x=x/2+1
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Equation x^2=6
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Equation (x+10)^2=(x-9)^2
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Equation (7-x)^2=(x+16)^2
- Express {x} in terms of y where:
- -11*x+4*y=-8
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- -14*x+1*y=3
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Identical expressions
- lg^ two x+lgx^2=log2- one
- lg squared x plus lgx squared equally logarithm of 2 minus 1
- lg to the power of two x plus lgx squared equally logarithm of 2 minus one
- lg2x+lgx2=log2-1
- lg²x+lgx²=log2-1
- lg to the power of 2x+lgx to the power of 2=log2-1
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Similar expressions
- lg^2x-lgx^2=log2-1
- (x^2+2x-1)(log2(x^2-3)+log2^-1(3^1/2-x))=0
- log(x+5)/log(2)-1=0
- lg^2x+lgx^2=log2+1
- (log((2-(13/x+5))^5)/log(3))=(log(1+(13/2*x-3))/log(3))-(log(2)/log(3))
- log^(2)(x/2)/log(2)-16=0
lg^2x+lgx^2=log2-1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2 2 log (x) + log (x) = log(2) - 1
$$\log{\left(x \right)}^{2} + \log{\left(x \right)}^{2} = -1 + \log{\left(2 \right)}$$
Rapid solution
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/ ___ ____________\ / ___ ____________\
|\/ 2 *\/ 1 - log(2) | |\/ 2 *\/ 1 - log(2) |
x1 = - I*sin|--------------------| + cos|--------------------|
\ 2 / \ 2 /
$$x_{1} = \cos{\left(\frac{\sqrt{2} \sqrt{1 - \log{\left(2 \right)}}}{2} \right)} - i \sin{\left(\frac{\sqrt{2} \sqrt{1 - \log{\left(2 \right)}}}{2} \right)}$$
/ ___ ____________\ / ___ ____________\
|\/ 2 *\/ 1 - log(2) | |\/ 2 *\/ 1 - log(2) |
x2 = I*sin|--------------------| + cos|--------------------|
\ 2 / \ 2 /
$$x_{2} = \cos{\left(\frac{\sqrt{2} \sqrt{1 - \log{\left(2 \right)}}}{2} \right)} + i \sin{\left(\frac{\sqrt{2} \sqrt{1 - \log{\left(2 \right)}}}{2} \right)}$$
x2 = cos(sqrt(2)*sqrt(1 - log(2))/2) + i*sin(sqrt(2)*sqrt(1 - log(2))/2)
Sum and product of roots
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sum
/ ___ ____________\ / ___ ____________\ / ___ ____________\ / ___ ____________\
|\/ 2 *\/ 1 - log(2) | |\/ 2 *\/ 1 - log(2) | |\/ 2 *\/ 1 - log(2) | |\/ 2 *\/ 1 - log(2) |
- I*sin|--------------------| + cos|--------------------| + I*sin|--------------------| + cos|--------------------|
\ 2 / \ 2 / \ 2 / \ 2 /
$$\left(\cos{\left(\frac{\sqrt{2} \sqrt{1 - \log{\left(2 \right)}}}{2} \right)} - i \sin{\left(\frac{\sqrt{2} \sqrt{1 - \log{\left(2 \right)}}}{2} \right)}\right) + \left(\cos{\left(\frac{\sqrt{2} \sqrt{1 - \log{\left(2 \right)}}}{2} \right)} + i \sin{\left(\frac{\sqrt{2} \sqrt{1 - \log{\left(2 \right)}}}{2} \right)}\right)$$
=
/ ___ ____________\
|\/ 2 *\/ 1 - log(2) |
2*cos|--------------------|
\ 2 /
$$2 \cos{\left(\frac{\sqrt{2} \sqrt{1 - \log{\left(2 \right)}}}{2} \right)}$$
product
/ / ___ ____________\ / ___ ____________\\ / / ___ ____________\ / ___ ____________\\ | |\/ 2 *\/ 1 - log(2) | |\/ 2 *\/ 1 - log(2) || | |\/ 2 *\/ 1 - log(2) | |\/ 2 *\/ 1 - log(2) || |- I*sin|--------------------| + cos|--------------------||*|I*sin|--------------------| + cos|--------------------|| \ \ 2 / \ 2 // \ \ 2 / \ 2 //
$$\left(\cos{\left(\frac{\sqrt{2} \sqrt{1 - \log{\left(2 \right)}}}{2} \right)} - i \sin{\left(\frac{\sqrt{2} \sqrt{1 - \log{\left(2 \right)}}}{2} \right)}\right) \left(\cos{\left(\frac{\sqrt{2} \sqrt{1 - \log{\left(2 \right)}}}{2} \right)} + i \sin{\left(\frac{\sqrt{2} \sqrt{1 - \log{\left(2 \right)}}}{2} \right)}\right)$$
=
1
$$1$$
1
Numerical answer
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x1 = 0.924262612040058 + 0.381757284128133*i
x2 = 0.924262612040058 - 0.381757284128133*i
x2 = 0.924262612040058 - 0.381757284128133*i