Question

How do you solve \[{{e}^{x}}=27\]?

Answer 1

Hint: In the given question, we have been asked to find the value of ‘x’ and t is given that\[{{e}^{x}}=27\]. In order to solve the question, first we need to take a log function on both sides of the equation. Then we need to apply power property of logarithm which states that \[{{\log }_{b}}{{\left( x \right)}^{n}}=n{{\log }_{b}}x\]. After that we need to simplify the equation and solve in a way we solve the general linear equations. We should know about the basic concepts of logarithmic function to get the required answer to this question.

Formula used: The power property of logarithm which states that \[{{\log }_{b}}{{\left( x \right)}^{n}}=n{{\log }_{b}}x\].

Complete step-by-step solution:
We have given that,
\[\Rightarrow {{e}^{x}}=27\]
Taking \[\ln \]to both the side of the equation, we get
\[\Rightarrow \ln {{e}^{x}}=\ln 27\]
Using the power property of logarithm which states that \[{{\log }_{b}}{{\left( x \right)}^{n}}=n{{\log }_{b}}x\].
Applying the power property of logarithm in the above equation, we get
\[\Rightarrow x\ln e=\ln 27\]
The value of\[\ln e=1\].
Putting the value of ln (e) = 1 in the equation, we get
\[\Rightarrow x\times 1=\ln 27\]
Simplifying the above equation, we get
\[\Rightarrow x=\ln 27\]
Therefore, the value of ‘x’ is equal to \[\ln 27\].
It is the required solution.

Note: In the given question, we need to find the value of ‘x’. To solve these types of questions, we used the basic formulas of logarithm. Students should always require to keep in mind all the formulae of logarithmic function for solving the question easily. After applying log formulae to the equation, we need to solve the equation in the way we solve general linear equations.