Question

How do you solve \[\ln x = 2\]?

Answer 1

Hint: In the given question, we have been given an expression. This expression contains a function. The function has a variable as its argument. We have to simplify the value of this expression. This can be easily done if we know the relation between the value function and the property of the function with the value.

Formula Used:
We are going to use the formula of logarithm, which is:
\[{\log _b}a = n \Rightarrow {b^n} = a\]

Complete step-by-step answer:
The given expression to be solved is:
\[\ln x = 2\]
\[{\log _e}\] is written as \[\ln \]
Hence, we have \[{\log _e}n = 2\]
And from the formula of logarithm, we have,
\[{\log _b}a = n \Rightarrow {b^n} = a\]
Thus, solving \[{\log _e}n = 2\], we get,
\[n = {e^2}\]

Additional Information:
The \[\log \] function has other basic properties too:
\[{\log _x}{x^n} = n\]
\[{\log _a}b = \dfrac{1}{{{{\log }_b}a}}\]

Note: In this question, to solve for the answer, we needed to know the properties of the logarithmic function. We needed to know how ln and log are related. In logarithms, we only need to know a few properties, and with that, we can solve any question involving any logarithm expression.