Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 3*x/3=(1-x)/2
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Equation tan(x)=-5
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Equation x^2=-81
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Equation sqrt(x-2)=x-4
- Express {x} in terms of y where:
- -13*x+15*y=1
- 11*x-6*y=-1
- -8*x-15*y=-12
- 18*x-15*y=-7
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Identical expressions
- -log(x)+log(two *x- one)/ two -log(three)/ two +log(two)=log(sqrt(four / five))
- minus logarithm of (x) plus logarithm of (2 multiply by x minus 1) divide by 2 minus logarithm of (3) divide by 2 plus logarithm of (2) equally logarithm of ( square root of (4 divide by 5))
- minus logarithm of (x) plus logarithm of (two multiply by x minus one) divide by two minus logarithm of (three) divide by two plus logarithm of (two) equally logarithm of ( square root of (four divide by five))
- -log(x)+log(2*x-1)/2-log(3)/2+log(2)=log(√(4/5))
- -log(x)+log(2x-1)/2-log(3)/2+log(2)=log(sqrt(4/5))
- -logx+log2x-1/2-log3/2+log2=logsqrt4/5
- -log(x)+log(2*x-1) divide by 2-log(3) divide by 2+log(2)=log(sqrt(4 divide by 5))
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Similar expressions
- -log(x)-log(2*x-1)/2-log(3)/2+log(2)=log(sqrt(4/5))
- -log(x)+log(2*x-1)/2+log(3)/2+log(2)=log(sqrt(4/5))
- -log(x)+log(2*x+1)/2-log(3)/2+log(2)=log(sqrt(4/5))
- -log(x)+log(2*x-1)/2-log(3)/2-log(2)=log(sqrt(4/5))
- log(x)+log(2*x-1)/2-log(3)/2+log(2)=log(sqrt(4/5))
-log(x)+log(2*x-1)/2-log(3)/2+log(2)=log(sqrt(4/5)) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
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log(2*x - 1) log(3) / _____\
-log(x) + ------------ - ------ + log(2) = log\\/ 4/5 /
2 2
$$\left(\left(- \log{\left(x \right)} + \frac{\log{\left(2 x - 1 \right)}}{2}\right) - \frac{\log{\left(3 \right)}}{2}\right) + \log{\left(2 \right)} = \log{\left(\sqrt{\frac{4}{5}} \right)}$$
Rapid solution
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____
5 \/ 10
x1 = - - ------
3 3
$$x_{1} = \frac{5}{3} - \frac{\sqrt{10}}{3}$$
____
5 \/ 10
x2 = - + ------
3 3
$$x_{2} = \frac{\sqrt{10}}{3} + \frac{5}{3}$$
x2 = sqrt(10)/3 + 5/3
Sum and product of roots
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sum
____ ____ 5 \/ 10 5 \/ 10 - - ------ + - + ------ 3 3 3 3
$$\left(\frac{5}{3} - \frac{\sqrt{10}}{3}\right) + \left(\frac{\sqrt{10}}{3} + \frac{5}{3}\right)$$
=
10/3
$$\frac{10}{3}$$
product
/ ____\ / ____\ |5 \/ 10 | |5 \/ 10 | |- - ------|*|- + ------| \3 3 / \3 3 /
$$\left(\frac{5}{3} - \frac{\sqrt{10}}{3}\right) \left(\frac{\sqrt{10}}{3} + \frac{5}{3}\right)$$
=
5/3
$$\frac{5}{3}$$
5/3
Numerical answer
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x1 = 2.72075922005613
x2 = 2.72075922005613 + 7.37644511638499e-15*i
x2 = 2.72075922005613 + 7.37644511638499e-15*i