Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation -x=4-3(3x-8)
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Equation x/9+x=-10/3
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Equation √(x^2-1)=2*x
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Equation 4(x-3)=x+6
- Express {x} in terms of y where:
- -6*x-20*y=8
- -9*x-15*y=-4
- 1*x+5*y=-11
- 12*x-14*y=20
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Identical expressions
- log(x+ five , five)-log(x+ three , five)+log(x+ one , five)= one +log(zero , six , five)
- logarithm of (x plus 5,5) minus logarithm of (x plus 3,5) plus logarithm of (x plus 1,5) equally 1 plus logarithm of (0,6,5)
- logarithm of (x plus five , five) minus logarithm of (x plus three , five) plus logarithm of (x plus one , five) equally one plus logarithm of (zero , six , five)
- logx+5,5-logx+3,5+logx+1,5=1+log0,6,5
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Similar expressions
- log(x+5,5)+log(x+3,5)+log(x+1,5)=1+log(0,6,5)
- log(x-5,5)-log(x+3,5)+log(x+1,5)=1+log(0,6,5)
- log(x+5,5)-log(x+3,5)+log(x+1,5)=1-log(0,6,5)
- log(x+5,5)-log(x+3,5)+log(x-1,5)=1+log(0,6,5)
- log(x+5,5)-log(x-3,5)+log(x+1,5)=1+log(0,6,5)
- log(x+5,5)-log(x+3,5)-log(x+1,5)=1+log(0,6,5)
log(x+5,5)-log(x+3,5)+log(x+1,5)=1+log(0,6,5) equation
The teacher will be very surprised to see your correct solution 😉
The solution
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[src]
log(3/5)
log(x + 11/2) - log(x + 7/2) + log(x + 3/2) = 1 + --------
log(5)
$$\left(- \log{\left(x + \frac{7}{2} \right)} + \log{\left(x + \frac{11}{2} \right)}\right) + \log{\left(x + \frac{3}{2} \right)} = \frac{\log{\left(\frac{3}{5} \right)}}{\log{\left(5 \right)}} + 1$$
Rapid solution
[src]
______________
1 / 2
------ / ------
log(5) / log(5)
7 3 \/ 16 + 3
x1 = - - + ------- + -------------------
2 2 2
$$x_{1} = - \frac{7}{2} + \frac{3^{\frac{1}{\log{\left(5 \right)}}}}{2} + \frac{\sqrt{3^{\frac{2}{\log{\left(5 \right)}}} + 16}}{2}$$
______________
1 / 2
------ / ------
log(5) / log(5)
7 3 \/ 16 + 3
x2 = - - + ------- - -------------------
2 2 2
$$x_{2} = - \frac{7}{2} - \frac{\sqrt{3^{\frac{2}{\log{\left(5 \right)}}} + 16}}{2} + \frac{3^{\frac{1}{\log{\left(5 \right)}}}}{2}$$
x2 = -7/2 - sqrt(3^(2/log(5)) + 16)/2 + 3^(1/log(5))/2
Sum and product of roots
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sum
______________ ______________
1 / 2 1 / 2
------ / ------ ------ / ------
log(5) / log(5) log(5) / log(5)
7 3 \/ 16 + 3 7 3 \/ 16 + 3
- - + ------- + ------------------- + - - + ------- - -------------------
2 2 2 2 2 2
$$\left(- \frac{7}{2} - \frac{\sqrt{3^{\frac{2}{\log{\left(5 \right)}}} + 16}}{2} + \frac{3^{\frac{1}{\log{\left(5 \right)}}}}{2}\right) + \left(- \frac{7}{2} + \frac{3^{\frac{1}{\log{\left(5 \right)}}}}{2} + \frac{\sqrt{3^{\frac{2}{\log{\left(5 \right)}}} + 16}}{2}\right)$$
=
1
------
log(5)
-7 + 3
$$-7 + 3^{\frac{1}{\log{\left(5 \right)}}}$$
product
/ ______________\ / ______________\ | 1 / 2 | | 1 / 2 | | ------ / ------ | | ------ / ------ | | log(5) / log(5) | | log(5) / log(5) | | 7 3 \/ 16 + 3 | | 7 3 \/ 16 + 3 | |- - + ------- + -------------------|*|- - + ------- - -------------------| \ 2 2 2 / \ 2 2 2 /
$$\left(- \frac{7}{2} + \frac{3^{\frac{1}{\log{\left(5 \right)}}}}{2} + \frac{\sqrt{3^{\frac{2}{\log{\left(5 \right)}}} + 16}}{2}\right) \left(- \frac{7}{2} - \frac{\sqrt{3^{\frac{2}{\log{\left(5 \right)}}} + 16}}{2} + \frac{3^{\frac{1}{\log{\left(5 \right)}}}}{2}\right)$$
=
1
------
log(5)
33 7*3
-- - ---------
4 2
$$\frac{33}{4} - \frac{7 \cdot 3^{\frac{1}{\log{\left(5 \right)}}}}{2}$$
33/4 - 7*3^(1/log(5))/2