Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation 9-4y=5y
- Equation 2/13+1/23=1,5-2/13
- Equation 2/3*8*x=0
- Equation z3+2*z2+z3-4*z-z2=0
- Express {x} in terms of y where:
- -2*x-18*y=7
- -19*x+16*y=-11
- -18*x+4*y=-11
- -19*x+7*y=17
- Derivative of:
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1/x+log(x)
- Limit of the function:
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1/x+log(x)
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Identical expressions
- log(y)+ one /y= one /x+log(x)
- logarithm of (y) plus 1 divide by y equally 1 divide by x plus logarithm of (x)
- logarithm of (y) plus one divide by y equally one divide by x plus logarithm of (x)
- logy+1/y=1/x+logx
- log(y)+1 divide by y=1 divide by x+log(x)
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Similar expressions
- log(y)+1/y=1/x-log(x)
- log(y)-1/y=1/x+log(x)
- (log(y)+1)/y=c-log(x)
log(y)+1/y=1/x+log(x) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
1 1
log(y) + - = - + log(x)
y x
$$\log{\left(y \right)} + \frac{1}{y} = \log{\left(x \right)} + \frac{1}{x}$$
The graph
Rapid solution
[src]
/ / -1 \\ / / -1 \\
| | --- || | | --- ||
| | y || | | y ||
| |-e || | |-e ||
| 1 + y*W|------|| | 1 + y*W|------||
| \ y /| | \ y /|
| ---------------| | ---------------|
| y | | y |
x1 = I*im\y*e / + re\y*e /
$$x_{1} = \operatorname{re}{\left(y e^{\frac{y W\left(- \frac{e^{- \frac{1}{y}}}{y}\right) + 1}{y}}\right)} + i \operatorname{im}{\left(y e^{\frac{y W\left(- \frac{e^{- \frac{1}{y}}}{y}\right) + 1}{y}}\right)}$$
x1 = re(y*exp((y*LambertW(-exp(-1/y)/y) + 1)/y)) + i*im(y*exp((y*LambertW(-exp(-1/y)/y) + 1)/y))
Sum and product of roots
[src]
sum
/ / -1 \\ / / -1 \\
| | --- || | | --- ||
| | y || | | y ||
| |-e || | |-e ||
| 1 + y*W|------|| | 1 + y*W|------||
| \ y /| | \ y /|
| ---------------| | ---------------|
| y | | y |
I*im\y*e / + re\y*e /
$$\operatorname{re}{\left(y e^{\frac{y W\left(- \frac{e^{- \frac{1}{y}}}{y}\right) + 1}{y}}\right)} + i \operatorname{im}{\left(y e^{\frac{y W\left(- \frac{e^{- \frac{1}{y}}}{y}\right) + 1}{y}}\right)}$$
=
/ / -1 \\ / / -1 \\
| | --- || | | --- ||
| | y || | | y ||
| |-e || | |-e ||
| 1 + y*W|------|| | 1 + y*W|------||
| \ y /| | \ y /|
| ---------------| | ---------------|
| y | | y |
I*im\y*e / + re\y*e /
$$\operatorname{re}{\left(y e^{\frac{y W\left(- \frac{e^{- \frac{1}{y}}}{y}\right) + 1}{y}}\right)} + i \operatorname{im}{\left(y e^{\frac{y W\left(- \frac{e^{- \frac{1}{y}}}{y}\right) + 1}{y}}\right)}$$
product
/ / -1 \\ / / -1 \\
| | --- || | | --- ||
| | y || | | y ||
| |-e || | |-e ||
| 1 + y*W|------|| | 1 + y*W|------||
| \ y /| | \ y /|
| ---------------| | ---------------|
| y | | y |
I*im\y*e / + re\y*e /
$$\operatorname{re}{\left(y e^{\frac{y W\left(- \frac{e^{- \frac{1}{y}}}{y}\right) + 1}{y}}\right)} + i \operatorname{im}{\left(y e^{\frac{y W\left(- \frac{e^{- \frac{1}{y}}}{y}\right) + 1}{y}}\right)}$$
=
/ / -1 \\ / / -1 \\
| | --- || | | --- ||
| | y || | | y ||
| |-e || | |-e ||
| 1 + y*W|------|| | 1 + y*W|------||
| \ y /| | \ y /|
| ---------------| | ---------------|
| y | | y |
I*im\y*e / + re\y*e /
$$\operatorname{re}{\left(y e^{\frac{y W\left(- \frac{e^{- \frac{1}{y}}}{y}\right) + 1}{y}}\right)} + i \operatorname{im}{\left(y e^{\frac{y W\left(- \frac{e^{- \frac{1}{y}}}{y}\right) + 1}{y}}\right)}$$
i*im(y*exp((1 + y*LambertW(-exp(-1/y)/y))/y)) + re(y*exp((1 + y*LambertW(-exp(-1/y)/y))/y))