Math CentralQuandaries & Queries


Question from James, a student:

How do you make x the subject of

ln (x) - x = ln (2)

Hi James.

You can't directly solve for x. Here's what you can do:

First, recognize that ln(2) is a small positive number.
Therefore ln(x) > x.

Second, recognize that ln(x) in the equation means that the domain is restricted to x > 0, because you can't take the logarithm of a non-positive number.

Look carefully at a graph of y = ln(x) and y = x. For what positive value(s) of x is ln(x) greater than x?

Stephen La Rocque.

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