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Equation 141*10^(-6)*x*3*sqrt(2)=sqrt((1-19881*10^(-12)*x^2)^2+9)
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Equation y+30*5=450
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Equation 8⋅(7+x)−5x=4x−64.
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Equation (x+3)-17=-20
- Express {x} in terms of y where:
- -2*x-20*y=4
- 15*x-17*y=-7
- -11*x-15*y=-7
- -5*x+17*y=-5
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Identical expressions
- log2/ three x-log3x=3
- logarithm of 2 divide by 3x minus logarithm of 3x equally 3
- logarithm of 2 divide by three x minus logarithm of 3x equally 3
- log2 divide by 3x-log3x=3
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Similar expressions
- log2/3x+log3x=3
log2/3x-log3x=3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
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[src]
log(2) ------*x - log(3*x) = 3 3
$$x \frac{\log{\left(2 \right)}}{3} - \log{\left(3 x \right)} = 3$$
Rapid solution
[src]
/ -3 \
|-e *log(2) |
-3*W|------------|
\ 9 /
x1 = ------------------
log(2)
$$x_{1} = - \frac{3 W\left(- \frac{\log{\left(2 \right)}}{9 e^{3}}\right)}{\log{\left(2 \right)}}$$
/ -3 \
|-e *log(2) |
-3*W|------------, -1|
\ 9 /
x2 = ----------------------
log(2)
$$x_{2} = - \frac{3 W_{-1}\left(- \frac{\log{\left(2 \right)}}{9 e^{3}}\right)}{\log{\left(2 \right)}}$$
x2 = -3*LambertW(-exp(-3)*log(2/9, -1)/log(2))
Sum and product of roots
[src]
sum
/ -3 \ / -3 \
|-e *log(2) | |-e *log(2) |
3*W|------------| 3*W|------------, -1|
\ 9 / \ 9 /
- ----------------- - ---------------------
log(2) log(2)
$$- \frac{3 W\left(- \frac{\log{\left(2 \right)}}{9 e^{3}}\right)}{\log{\left(2 \right)}} - \frac{3 W_{-1}\left(- \frac{\log{\left(2 \right)}}{9 e^{3}}\right)}{\log{\left(2 \right)}}$$
=
/ -3 \ / -3 \
|-e *log(2) | |-e *log(2) |
3*W|------------| 3*W|------------, -1|
\ 9 / \ 9 /
- ----------------- - ---------------------
log(2) log(2)
$$- \frac{3 W\left(- \frac{\log{\left(2 \right)}}{9 e^{3}}\right)}{\log{\left(2 \right)}} - \frac{3 W_{-1}\left(- \frac{\log{\left(2 \right)}}{9 e^{3}}\right)}{\log{\left(2 \right)}}$$
product
/ -3 \ / -3 \
|-e *log(2) | |-e *log(2) |
-3*W|------------| -3*W|------------, -1|
\ 9 / \ 9 /
------------------*----------------------
log(2) log(2)
$$- \frac{3 W\left(- \frac{\log{\left(2 \right)}}{9 e^{3}}\right)}{\log{\left(2 \right)}} \left(- \frac{3 W_{-1}\left(- \frac{\log{\left(2 \right)}}{9 e^{3}}\right)}{\log{\left(2 \right)}}\right)$$
=
/ -3 \ / -3 \
|-e *log(2) | |-e *log(2) |
9*W|------------|*W|------------, -1|
\ 9 / \ 9 /
-------------------------------------
2
log (2)
$$\frac{9 W\left(- \frac{\log{\left(2 \right)}}{9 e^{3}}\right) W_{-1}\left(- \frac{\log{\left(2 \right)}}{9 e^{3}}\right)}{\log{\left(2 \right)}^{2}}$$
9*LambertW(-exp(-3)*log(2)/9)*LambertW(-exp(-3)*log(2)/9, -1)/log(2)^2