Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (x-2)/(x-7)=5/8
-
Equation 6/(x+5)=-5
- Equation z^2+3+4*i=0
-
Equation 3x-2(3x+4)=10
- Express {x} in terms of y where:
- -14*x+10*y=19
- -18*x+8*y=-2
- -6*x+12*y=11
- 7*x-1*y=0
-
Identical expressions
- sqrt(three ^(x+ three))- twenty-seven ^x= zero
- square root of (3 to the power of (x plus 3)) minus 27 to the power of x equally 0
- square root of (three to the power of (x plus three)) minus twenty minus seven to the power of x equally zero
- √(3^(x+3))-27^x=0
- sqrt(3(x+3))-27x=0
- sqrt3x+3-27x=0
- sqrt3^x+3-27^x=0
- sqrt(3^(x+3))-27^x=O
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Similar expressions
- sqrt(3^(x+3))+27^x=0
- sqrt(3^(x-3))-27^x=0
sqrt(3^(x+3))-27^x=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Rapid solution
[src]
x1 = 3/5
$$x_{1} = \frac{3}{5}$$
log(27) 4*pi*I
x2 = -------- - --------
5*log(3) 5*log(3)
$$x_{2} = \frac{\log{\left(27 \right)}}{5 \log{\left(3 \right)}} - \frac{4 i \pi}{5 \log{\left(3 \right)}}$$
log(27) 4*pi*I
x3 = -------- + --------
5*log(3) 5*log(3)
$$x_{3} = \frac{\log{\left(27 \right)}}{5 \log{\left(3 \right)}} + \frac{4 i \pi}{5 \log{\left(3 \right)}}$$
x3 = log(27)/(5*log(3)) + 4*i*pi/(5*log(3))
Sum and product of roots
[src]
sum
3 log(27) 4*pi*I log(27) 4*pi*I - + -------- - -------- + -------- + -------- 5 5*log(3) 5*log(3) 5*log(3) 5*log(3)
$$\left(\frac{3}{5} + \left(\frac{\log{\left(27 \right)}}{5 \log{\left(3 \right)}} - \frac{4 i \pi}{5 \log{\left(3 \right)}}\right)\right) + \left(\frac{\log{\left(27 \right)}}{5 \log{\left(3 \right)}} + \frac{4 i \pi}{5 \log{\left(3 \right)}}\right)$$
=
3 2*log(27) - + --------- 5 5*log(3)
$$\frac{3}{5} + \frac{2 \log{\left(27 \right)}}{5 \log{\left(3 \right)}}$$
product
/log(27) 4*pi*I \
3*|-------- - --------|
\5*log(3) 5*log(3)/ /log(27) 4*pi*I \
-----------------------*|-------- + --------|
5 \5*log(3) 5*log(3)/
$$\frac{3 \left(\frac{\log{\left(27 \right)}}{5 \log{\left(3 \right)}} - \frac{4 i \pi}{5 \log{\left(3 \right)}}\right)}{5} \left(\frac{\log{\left(27 \right)}}{5 \log{\left(3 \right)}} + \frac{4 i \pi}{5 \log{\left(3 \right)}}\right)$$
=
2
27 48*pi
--- + -----------
125 2
125*log (3)
$$\frac{27}{125} + \frac{48 \pi^{2}}{125 \log{\left(3 \right)}^{2}}$$
27/125 + 48*pi^2/(125*log(3)^2)
Numerical answer
[src]
x1 = -62.1177727266686
x2 = -100.117772726669
x3 = -96.1177727266686
x4 = -72.1177727266686
x5 = -60.1177727266686
x6 = -88.1177727266686
x7 = -92.1177727266686
x8 = -58.1177727266686
x9 = -132.117772726669
x10 = -70.1177727266686
x11 = -116.117772726669
x12 = -104.117772726669
x13 = -106.117772726669
x14 = -102.117772726669
x15 = -122.117772726669
x16 = -128.117772726669
x17 = -120.117772726669
x18 = -130.117772726669
x19 = -136.117772726669
x20 = -68.1177727266686
x21 = -134.117772726669
x22 = -78.1177727266686
x23 = -80.1177727266686
x24 = -74.1177727266686
x25 = -76.1177727266686
x26 = -84.1177727266686
x27 = -126.117772726669
x28 = -138.117772726669
x29 = -82.1177727266686
x30 = -98.1177727266686
x31 = 0.6
x32 = -114.117772726669
x33 = -110.117772726669
x34 = -90.1177727266686
x35 = -112.117772726669
x36 = -124.117772726669
x37 = -64.1177727266686
x38 = -56.1177727266686
x39 = -86.1177727266686
x40 = -66.1177727266686
x41 = -118.117772726669
x42 = -54.1177727266686
x43 = -108.117772726669
x44 = -94.1177727266686
x44 = -94.1177727266686