Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation sin(x)=cos(x)
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Equation cos(x)=(-1/2)
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Equation sin(x-1)=0
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Equation 4*x^2-25=0
- Express {x} in terms of y where:
- 12*x+5*y=7
- -10*x+14*y=20
- -8*x-17*y=-12
- -6*x+17*y=-15
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Identical expressions
- three * two ^(x+ one)- two * five ^(x- two)= five ^(x)+ two ^(x- one)
- 3 multiply by 2 to the power of (x plus 1) minus 2 multiply by 5 to the power of (x minus 2) equally 5 to the power of (x) plus 2 to the power of (x minus 1)
- three multiply by two to the power of (x plus one) minus two multiply by five to the power of (x minus two) equally five to the power of (x) plus two to the power of (x minus one)
- 3*2(x+1)-2*5(x-2)=5(x)+2(x-1)
- 3*2x+1-2*5x-2=5x+2x-1
- 32^(x+1)-25^(x-2)=5^(x)+2^(x-1)
- 32(x+1)-25(x-2)=5(x)+2(x-1)
- 32x+1-25x-2=5x+2x-1
- 32^x+1-25^x-2=5^x+2^x-1
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Similar expressions
- 3*2^(x+1)+2*5^(x-2)=5^(x)+2^(x-1)
- 3*2^(x+1)-2*5^(x-2)=5^(x)+2^(x+1)
- 3*2^(x+1)-2*5^(x-2)=5^(x)-2^(x-1)
- 3*2^(x-1)-2*5^(x-2)=5^(x)+2^(x-1)
- 3*2^(x+1)-2*5^(x+2)=5^(x)+2^(x-1)
3*2^(x+1)-2*5^(x-2)=5^(x)+2^(x-1) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
x + 1 x - 2 x x - 1 3*2 - 2*5 = 5 + 2
$$3 \cdot 2^{x + 1} - 2 \cdot 5^{x - 2} = 2^{x - 1} + 5^{x}$$
Rapid solution
[src]
/ 1 \
| --------|
| log(2/5)|
|/275\ |
x1 = -log||---| |
\\ 54/ /
$$x_{1} = - \log{\left(\left(\frac{275}{54}\right)^{\frac{1}{\log{\left(\frac{2}{5} \right)}}} \right)}$$
/ 1 \
| --------|
| log(2/5)|
|/ 54\ |
x2 = log||---| |
\\275/ /
$$x_{2} = \log{\left(\left(\frac{54}{275}\right)^{\frac{1}{\log{\left(\frac{2}{5} \right)}}} \right)}$$
x2 = log((54/275)^(1/log(2/5)))
Sum and product of roots
[src]
sum
/ 1 \ / 1 \
| --------| | --------|
| log(2/5)| | log(2/5)|
|/275\ | |/ 54\ |
- log||---| | + log||---| |
\\ 54/ / \\275/ /
$$- \log{\left(\left(\frac{275}{54}\right)^{\frac{1}{\log{\left(\frac{2}{5} \right)}}} \right)} + \log{\left(\left(\frac{54}{275}\right)^{\frac{1}{\log{\left(\frac{2}{5} \right)}}} \right)}$$
=
/ 1 \ / 1 \
| --------| | --------|
| log(2/5)| | log(2/5)|
|/275\ | |/ 54\ |
- log||---| | + log||---| |
\\ 54/ / \\275/ /
$$- \log{\left(\left(\frac{275}{54}\right)^{\frac{1}{\log{\left(\frac{2}{5} \right)}}} \right)} + \log{\left(\left(\frac{54}{275}\right)^{\frac{1}{\log{\left(\frac{2}{5} \right)}}} \right)}$$
product
/ 1 \ / 1 \
| --------| | --------|
| log(2/5)| | log(2/5)|
|/275\ | |/ 54\ |
-log||---| |*log||---| |
\\ 54/ / \\275/ /
$$- \log{\left(\left(\frac{275}{54}\right)^{\frac{1}{\log{\left(\frac{2}{5} \right)}}} \right)} \log{\left(\left(\frac{54}{275}\right)^{\frac{1}{\log{\left(\frac{2}{5} \right)}}} \right)}$$
=
2 2 / log(2916)\
log (54) + log (275) - log\275 /
----------------------------------------
2 2 / log(4)\
log (2) + log (5) - log\5 /
$$\frac{- \log{\left(275^{\log{\left(2916 \right)}} \right)} + \log{\left(54 \right)}^{2} + \log{\left(275 \right)}^{2}}{- \log{\left(5^{\log{\left(4 \right)}} \right)} + \log{\left(2 \right)}^{2} + \log{\left(5 \right)}^{2}}$$
(log(54)^2 + log(275)^2 - log(275^log(2916)))/(log(2)^2 + log(5)^2 - log(5^log(4)))
Numerical answer
[src]
x1 = -76.176760093132
x2 = -62.1767600931321
x3 = -108.176760093132
x4 = -96.176760093132
x5 = -98.176760093132
x6 = -54.1767600932947
x7 = -126.176760093132
x8 = -42.176769787628
x9 = -122.176760093132
x10 = -114.176760093132
x11 = -46.17676034131
x12 = 1.77649625220247
x13 = -52.1767600941486
x14 = -64.176760093132
x15 = -124.176760093132
x16 = -74.176760093132
x17 = -112.176760093132
x18 = -70.176760093132
x19 = -78.176760093132
x20 = -102.176760093132
x21 = -120.176760093132
x22 = -86.176760093132
x23 = -82.176760093132
x24 = -88.176760093132
x25 = -94.176760093132
x26 = -80.176760093132
x27 = -66.176760093132
x28 = -92.176760093132
x29 = -104.176760093132
x30 = -56.1767600931581
x31 = -118.176760093132
x32 = -44.1767616442454
x33 = -128.176760093132
x34 = -84.176760093132
x35 = -72.176760093132
x36 = -50.1767600994854
x37 = -106.176760093132
x38 = -100.176760093132
x39 = -116.176760093132
x40 = -60.1767600931327
x41 = -48.1767601328405
x42 = -130.176760093132
x43 = -58.1767600931362
x44 = -68.176760093132
x45 = -110.176760093132
x46 = -90.176760093132
x46 = -90.176760093132