Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation cos(x)=sqrt(3)/2
- Equation lg^(2)(x)=lg(10x)
- Equation (x+4)/(5*x+9)=(x+4)/(4*x-5)
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Equation (K+11)/23=27
- Express {x} in terms of y where:
- 9*x-18*y=6
- 15*x+15*y=16
- -4*x+18*y=-14
- 14*x-16*y=14
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Identical expressions
- lg^(two)(x)=lg(10x)
- lg to the power of (2)(x) equally lg(10x)
- lg to the power of (two)(x) equally lg(10x)
- lg(2)(x)=lg(10x)
- lg2x=lg10x
- lg^2x=lg10x
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Similar expressions
- (lgx^2)^2+lg10x-6=0
- lg(10*x)^2+lg(x)=0
- lg^2(x+1)-lg(x+1)-2=0
- lg^10(x^2-3)=0
- lg^2(x^2)+lg(10*x)-6=0
lg^(2)(x)=lg(10x) equation
The teacher will be very surprised to see your correct solution 😉
The solution
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2 log (x) = log(10*x)
$$\log{\left(x \right)}^{2} = \log{\left(10 x \right)}$$
Sum and product of roots
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sum
_______________ _______________ 1 \/ 1 + 4*log(10) 1 \/ 1 + 4*log(10) - - ----------------- - + ----------------- 2 2 2 2 e + e
$$e^{\frac{1}{2} - \frac{\sqrt{1 + 4 \log{\left(10 \right)}}}{2}} + e^{\frac{1}{2} + \frac{\sqrt{1 + 4 \log{\left(10 \right)}}}{2}}$$
=
_______________ _______________ 1 \/ 1 + 4*log(10) 1 \/ 1 + 4*log(10) - + ----------------- - - ----------------- 2 2 2 2 e + e
$$e^{\frac{1}{2} - \frac{\sqrt{1 + 4 \log{\left(10 \right)}}}{2}} + e^{\frac{1}{2} + \frac{\sqrt{1 + 4 \log{\left(10 \right)}}}{2}}$$
product
_______________ _______________ 1 \/ 1 + 4*log(10) 1 \/ 1 + 4*log(10) - - ----------------- - + ----------------- 2 2 2 2 e *e
$$\frac{e^{\frac{1}{2} + \frac{\sqrt{1 + 4 \log{\left(10 \right)}}}{2}}}{e^{- \frac{1}{2} + \frac{\sqrt{1 + 4 \log{\left(10 \right)}}}{2}}}$$
=
E
$$e$$
E
Rapid solution
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_______________
1 \/ 1 + 4*log(10)
- - -----------------
2 2
x1 = e
$$x_{1} = e^{\frac{1}{2} - \frac{\sqrt{1 + 4 \log{\left(10 \right)}}}{2}}$$
_______________
1 \/ 1 + 4*log(10)
- + -----------------
2 2
x2 = e
$$x_{2} = e^{\frac{1}{2} + \frac{\sqrt{1 + 4 \log{\left(10 \right)}}}{2}}$$
x2 = exp(1/2 + sqrt(1 + 4*log(10))/2)