# how can i solve x/ln(n)=100

#### danielhaish

##### New member
Hi i am worikng on some encryption program and i need to solve this problem thereis any chance thus is possible using w Limburg function and how

#### Subhotosh Khan

##### Super Moderator
Staff member
Hi i am worikng on some encryption program and i need to solve this problem thereis any chance thus is possible using w Limburg function and how
The expression in the subject line

x/lenx=n

does not make any sense to me. Please "correct" it and re-post.

#### danielhaish

##### New member
The expression in the subject line

x/lenx=n

does not make any sense to me. Please "correct" it and re-post.
is it ok now i just need alitle help in solving this kind of problem

#### Subhotosh Khan

##### Super Moderator
Staff member
is it ok now i just need alitle help in solving this kind of problem
Sorry .... I still cannot decipher your problem statement.

What is "len"?

#### danielhaish

##### New member
I am sory I meant ln

#### danielhaish

##### New member
i cant edit it right now from some reason
so this is the equation x/ln(x)=n

#### MarkFL

##### Super Moderator
Staff member
I would use the function:

$$\displaystyle f(x)=x-n\ln(x)=0$$

And use the Newton-Raphson method to recursively find the root to a desired accuracy.

#### danielhaish

##### New member
hi i olso got something like that but cant solve it
nt-e^t=0
I would use the function:

$$\displaystyle f(x)=x-n\ln(x)=0$$

And use the Newton-Raphson method to recursively find the root to a desired accuracy.
in the end i simplified it to 100t-e^t while t=len(x)
and i use regula falsi method tenx

#### HallsofIvy

##### Elite Member
To solve $$\displaystyle \frac{x}{ln(x)}= n$$ for x, write it as $$\displaystyle \frac{ln(x)}{x}= \frac{1}{n}$$ and let y= 1/x. The equation becomes $$\displaystyle y ln(1/y)= -y ln(y)= \frac{1}{n}$$ or $$\displaystyle y ln(y)= -\frac{1}{n}$$. NOW you can use Lambert's W function that I think you intended in your first post: $$\displaystyle y= W\left(-\frac{1}{n}\right)$$ and then $$\displaystyle x= \frac{1}{W\left(-\frac{1}{n}\right)}$$.

#### danielhaish

##### New member
To solve $$\displaystyle \frac{x}{ln(x)}= n$$ for x, write it as $$\displaystyle \frac{ln(x)}{x}= \frac{1}{n}$$ and let y= 1/x. The equation becomes $$\displaystyle y ln(1/y)= -y ln(y)= \frac{1}{n}$$ or $$\displaystyle y ln(y)= -\frac{1}{n}$$. NOW you can use Lambert's W function that I think you intended in your first post: $$\displaystyle y= W\left(-\frac{1}{n}\right)$$ and then $$\displaystyle x= \frac{1}{W\left(-\frac{1}{n}\right)}$$.
tenx it make my program alot more simple becuase now i just use function that allready exsits

#### danielhaish

##### New member
To solve $$\displaystyle \frac{x}{ln(x)}= n$$ for x, write it as $$\displaystyle \frac{ln(x)}{x}= \frac{1}{n}$$ and let y= 1/x. The equation becomes $$\displaystyle y ln(1/y)= -y ln(y)= \frac{1}{n}$$ or $$\displaystyle y ln(y)= -\frac{1}{n}$$. NOW you can use Lambert's W function that I think you intended in your first post: $$\displaystyle y= W\left(-\frac{1}{n}\right)$$ and then $$\displaystyle x= \frac{1}{W\left(-\frac{1}{n}\right)}$$.
hi i tried possed n=10 and then take the x and poss it in education and it doesn't return 10 it return 4