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How can I solve the Logarithm : In(1/x) = 10 ???

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2 Answers

Natural log is log base e, so ln(x) = 10 means that x is e raised to the 10th power.

Here ln(1/x) = 10, so 1/x = e10.

Now simple algebra will suffice:

x = 1/e10 = e-10

The definition of a logarithm will lead you to the solution.

If b is the base of the logarithm, then:

blogb(a) = a

e is the base for natural logarithms, so

eln(1/x) = 1/x

Then, since we know that ln(1/x) is 10, 

eln(1/x) = e10 = 1/x

1/x = e10

x = 1/e10 

x = e-10