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

Question

Could anyone pls help me?? Thank you!!!

Answer 1

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

Answer 2

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) =} e¹⁰ = 1/x

1/x = e¹⁰

x = 1/e¹⁰ 

x = e^-10