MHB Is n a Variable or Fixed Constant in the Equation n^lnx = x?

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In the equation n^ln(x) = x, n is treated as a fixed constant, typically a positive value not equal to 1. The correct identity is a^log_a(x) = x, where a represents a fixed base. The discussion clarifies that for suitable values of n, it can be shown that n equals e when applying logarithmic properties. The conclusion confirms that n is indeed constant in this context. Understanding these properties is essential for solving logarithmic equations accurately.
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Hi,

I learned today that n^lx = x

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

Thanks ,

Tim
 
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The actual identity is:

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

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