Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^(lgx+1)=100
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Equation (4cos2x-9sinx-4)lg(-cosx)=0
- Equation x^4+5x^2-36=0
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Equation 2sinx=5cosx
- Express {x} in terms of y where:
- 5*x-5*y=20
- 8*x-7*y=-13
- 15*x-15*y=16
- 9*x+18*y=6
- Sum of series:
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100
- Integral of d{x}:
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100
- Canonical form:
- 100
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Identical expressions
- x^(lgx+ one)= one hundred
- x to the power of (lgx plus 1) equally 100
- x to the power of (lgx plus one) equally one hundred
- x(lgx+1)=100
- xlgx+1=100
- x^lgx+1=100
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Similar expressions
- x^(lgx-1)=100
x^(lgx+1)=100 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Rapid solution
[src]
_______________
1 \/ 1 + 8*log(10)
- - + -----------------
2 2
x_1 = e
$$x_{1} = e^{- \frac{1}{2} + \frac{\sqrt{1 + 8 \log{\left(10 \right)}}}{2}}$$
_______________
1 \/ 1 + 8*log(10)
- - - -----------------
2 2
x_2 = e
$$x_{2} = e^{- \frac{\sqrt{1 + 8 \log{\left(10 \right)}}}{2} - \frac{1}{2}}$$
Sum and product of roots
[src]
sum
_______________ _______________ 1 \/ 1 + 8*log(10) 1 \/ 1 + 8*log(10) - - + ----------------- - - - ----------------- 2 2 2 2 e + e
$$\left(e^{- \frac{1}{2} + \frac{\sqrt{1 + 8 \log{\left(10 \right)}}}{2}}\right) + \left(e^{- \frac{\sqrt{1 + 8 \log{\left(10 \right)}}}{2} - \frac{1}{2}}\right)$$
=
_______________ _______________ 1 \/ 1 + 8*log(10) 1 \/ 1 + 8*log(10) - - + ----------------- - - - ----------------- 2 2 2 2 e + e
$$e^{- \frac{\sqrt{1 + 8 \log{\left(10 \right)}}}{2} - \frac{1}{2}} + e^{- \frac{1}{2} + \frac{\sqrt{1 + 8 \log{\left(10 \right)}}}{2}}$$
product
_______________ _______________ 1 \/ 1 + 8*log(10) 1 \/ 1 + 8*log(10) - - + ----------------- - - - ----------------- 2 2 2 2 e * e
$$\left(e^{- \frac{1}{2} + \frac{\sqrt{1 + 8 \log{\left(10 \right)}}}{2}}\right) * \left(e^{- \frac{\sqrt{1 + 8 \log{\left(10 \right)}}}{2} - \frac{1}{2}}\right)$$
=
-1 e
$$e^{-1}$$
Numerical answer
[src]
x1 = -6.05421280359705 - 10.9558439432548*i
x2 = 5.4928380566125
x3 = 5.4928380566125
x3 = 5.4928380566125
The graph