Hint

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X in degree X

Fun

We were looking for the X value, which corresponds to some (2 and / or 4) value of function t

Let's take a look at the inverse function X = X (t) . Rewrite initial equation as:

Let's find an extremum.
To make things easier, let's write down the logarithms of the left and right sides.

Now, let's differentiate:

Extremum condition is:

That is, the extremum (maximum) is at:

You can analyze further, but now it is easier to plot the dependence X = X (t)

So, it is clear that X can take values from 0 to

= 1.44466786100977 (approximately 😉)

Here e = 2.71828182845904 (approximately 😉)

That is, the domain as well as the range of the function both are very limited 👍😁👍

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X in degree X

Fun

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