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- Equation:
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Equation (x-4)^2-x^2=0
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Equation 1/(x-2)^2-1/(x-2)-6=0
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Equation 25x^2-1=0
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Equation x^2+4x+4=0
- Express {x} in terms of y where:
- 10*x-15*y=16
- -1*x-17*y=-12
- 14*x-16*y=19
- 18*x+1*y=-11
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Identical expressions
- logx27-log27x²= one
- logarithm of x27 minus logarithm of 27x² equally 1
- logarithm of x27 minus logarithm of 27x² equally one
-
Similar expressions
- logx27+log27x²=1
logx27-log27x²=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2 log(x)*27 - log (27*x) = 1
$$27 \log{\left(x \right)} - \log{\left(27 x \right)}^{2} = 1$$
Rapid solution
[src]
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27 \/ 725 - log(38662196978715633273404758790074316960214213096178319621856934259807530937321861485192508542873470637501160980081794035970219670238407078788135931371782481)
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2 2
e
x1 = --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
27
$$x_{1} = \frac{e^{\frac{27}{2} - \frac{\sqrt{725 - \log{\left(38662196978715633273404758790074316960214213096178319621856934259807530937321861485192508542873470637501160980081794035970219670238407078788135931371782481 \right)}}}{2}}}{27}$$
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27 \/ 725 - log(38662196978715633273404758790074316960214213096178319621856934259807530937321861485192508542873470637501160980081794035970219670238407078788135931371782481)
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2 2
e
x2 = --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
27
$$x_{2} = \frac{e^{\frac{\sqrt{725 - \log{\left(38662196978715633273404758790074316960214213096178319621856934259807530937321861485192508542873470637501160980081794035970219670238407078788135931371782481 \right)}}}{2} + \frac{27}{2}}}{27}$$
x2 = exp(sqrt(725 - log(38662196978715633273404758790074316960214213096178319621856934259807530937321861485192508542873470637501160980081794035970219670238407078788135931371782481))/2 + 27/2)/27
Sum and product of roots
[src]
sum
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27 \/ 725 - log(38662196978715633273404758790074316960214213096178319621856934259807530937321861485192508542873470637501160980081794035970219670238407078788135931371782481) 27 \/ 725 - log(38662196978715633273404758790074316960214213096178319621856934259807530937321861485192508542873470637501160980081794035970219670238407078788135931371782481)
-- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------- -- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2 2 2
e e
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
27 27
$$\frac{e^{\frac{27}{2} - \frac{\sqrt{725 - \log{\left(38662196978715633273404758790074316960214213096178319621856934259807530937321861485192508542873470637501160980081794035970219670238407078788135931371782481 \right)}}}{2}}}{27} + \frac{e^{\frac{\sqrt{725 - \log{\left(38662196978715633273404758790074316960214213096178319621856934259807530937321861485192508542873470637501160980081794035970219670238407078788135931371782481 \right)}}}{2} + \frac{27}{2}}}{27}$$
=
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27 \/ 725 - log(38662196978715633273404758790074316960214213096178319621856934259807530937321861485192508542873470637501160980081794035970219670238407078788135931371782481) 27 \/ 725 - log(38662196978715633273404758790074316960214213096178319621856934259807530937321861485192508542873470637501160980081794035970219670238407078788135931371782481)
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2 2 2 2
e e
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27 27
$$\frac{e^{\frac{27}{2} - \frac{\sqrt{725 - \log{\left(38662196978715633273404758790074316960214213096178319621856934259807530937321861485192508542873470637501160980081794035970219670238407078788135931371782481 \right)}}}{2}}}{27} + \frac{e^{\frac{\sqrt{725 - \log{\left(38662196978715633273404758790074316960214213096178319621856934259807530937321861485192508542873470637501160980081794035970219670238407078788135931371782481 \right)}}}{2} + \frac{27}{2}}}{27}$$
product
________________________________________________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________________________________________________
27 \/ 725 - log(38662196978715633273404758790074316960214213096178319621856934259807530937321861485192508542873470637501160980081794035970219670238407078788135931371782481) 27 \/ 725 - log(38662196978715633273404758790074316960214213096178319621856934259807530937321861485192508542873470637501160980081794035970219670238407078788135931371782481)
-- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------- -- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2 2 2
e e
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------*--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
27 27
$$\frac{e^{\frac{27}{2} - \frac{\sqrt{725 - \log{\left(38662196978715633273404758790074316960214213096178319621856934259807530937321861485192508542873470637501160980081794035970219670238407078788135931371782481 \right)}}}{2}}}{27} \frac{e^{\frac{\sqrt{725 - \log{\left(38662196978715633273404758790074316960214213096178319621856934259807530937321861485192508542873470637501160980081794035970219670238407078788135931371782481 \right)}}}{2} + \frac{27}{2}}}{27}$$
=
27 e --- 729
$$\frac{e^{27}}{729}$$
exp(27)/729
Numerical answer
[src]
x1 = 401009320.062243
x2 = 401009320.062243 - 2.26963455783499e-18*i
x3 = 401009320.06224 + 2.47146841488962e-7*i
x4 = 401009320.062243 - 2.04504820208898e-19*i
x5 = 1.81999006255669
x6 = 401009320.062243 - 2.0396941085459e-18*i
x7 = 401009320.062243 + 1.85905642578797e-19*i
x8 = 401009320.062243 - 2.52230588573904e-19*i
x9 = 401009320.062243 + 1.96712052962989e-18*i
x10 = 401009320.062243 - 1.85499563484497e-19*i
x11 = 401009320.062243 + 3.71550210158245e-19*i
x11 = 401009320.062243 + 3.71550210158245e-19*i