# n^lnx = x simple question

#### tmt

##### Active member
Hi,

I learned today that n^lx = x

Is this where n is a variable a a fixed constant?

Thanks ,

Tim

#### MarkFL

Staff member
The actual identity is:

$$\displaystyle a^{\log_a(x)}=x$$

For suitable values of $a$, usually taken to be a positive fixed value not equal to 1.

#### mente oscura

##### Well-known member
Hi,

I learned today that n^lx = x

Is this where n is a variable a a fixed constant?

Thanks ,

Tim
Hello.

But, yes, it is constant:

$$\log_e(x) \ \log_e(n)=\log_e(x) \rightarrow{}n=e$$

It is correct, isn't it?

Regards.