Question

How do you solve \[\ln x=2.7\]?

Answer 1

Hint: From the question given, we have been asked to solve \[\ln x=2.7\]. We can solve the above-given question by using some basic formulae or properties of logarithms. If the given question is not solved by using the basic formulae or properties of logarithms, then we have to do certain transformations or substitutions to get the given question solved.

Complete step by step answer:
From the question given, we had been given that \[\ln x=2.7\]
We can clearly observe that the given question cannot be solved by any of the direct formulae or direct property. So, here we have to do some transformation to the given question.
We know that the operation inverse to the logarithm is the exponential.
Then we can apply the exponential on both sides of the given equation.
By applying the exponential on both sides of the equation, we get,
\[\ln x=2.7\]
\[\Rightarrow {{e}^{\ln x}}={{e}^{2.7}}\]
And, because the exponential is the opposite of the logarithm, we have
\[{{e}^{\ln x}}={{e}^{2.7}}\]
\[\Rightarrow x={{e}^{2.7}}\]
We know that the value of \[e=2.718\].
By substituting the value of \[e=2.718\] in the above equation, we get \[x={{\left( 2.718 \right)}^{2.7}}\]
On simplifying furthermore by using a pocket calculator, we get
\[x={{\left( 2.718 \right)}^{2.7}}\]
\[\Rightarrow x\approx 14.88\]
Hence, the given question is solved by transforming it into exponentials.

Note:
We should be well known about the logarithms. Also, we should be well known about the basic properties and basic formulae of logarithms. We should know how to transform the given question into another form if the question is not being solved in its original form. We should be also very careful while doing the calculation. This can be simply answered as \[\ln x=2.7\Rightarrow {{e}^{2.7}}=x\] .