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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 = e^{10}.

Now simple algebra will suffice:

x = 1/e^{10} = e^{-10}

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

If b is the base of the logarithm, then:

b^{logb(a)} = a

e is the base for natural logarithms, so

e^{ln(1/x)} = 1/x

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

e^{ln(1/x) =} e^{10} = 1/x

1/x = e^{10}

x = 1/e^{10}

x = e^{-10}