Excel, 19 bytes

=9^9*(A1^(1/9^9)-1)

Input in cell A1. The choice of 9^9 is sufficient for the given test cases and required accuracy.

Excel, 19 16 bytes

With many thanks to Dominic van Essen for the 3-byte save:

=1E9*(A1^1E-9-1)

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=9^9*(A1^(1/9^9)-1)

Input in cell A1. The choice of 1E9 (i.e. 1000000000) is sufficient for the given test cases and required accuracy.