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Exercise

$x^2\left(1+ln\left(y\right)\right)dx=0$

Step-by-step Solution

1

Divide both sides of the equation by $x^2$

$\left(1+\ln\left(y\right)\right)dx=0$
2

Divide both sides of the equation by $dx$

$1+\ln\left(y\right)=0$
3

We need to isolate the dependent variable $y$, we can do that by simultaneously subtracting $1$ from both sides of the equation

$\ln\left(y\right)=-1$
4

Take the variable outside of the logarithm

$e^{\ln\left(y\right)}=e^{-1}$
5

Simplifying the logarithm

$y=e^{-1}$

Final answer to the exercise

$y=e^{-1}$

Try other ways to solve this exercise

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Similar Questions Solved

$\log\left(x\right)=3$

$2log\left(x\right)-log\left(x+6\right)=0$

$\log_3\left(x+4\right)+\log_3\left(x-4\right)=2$

$\log\left(4X^2\right)=128$

$\log_x\left(64\right)=3$

$\log_2\left(x-2\right)+\log_2\left(x+1\right)=2$

$2\cdot log\left(x\right)-1\cdot log\left(x+6\right)=0$

Main Topic: Logarithmic Equations

Are those equations in which the unknown variable appears within a logarithm.

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