Question

How do you solve \[3{{e}^{x}}=122\]?

Answer 1

Hint: In this problem, we have to solve the given exponential expression to find the value of x. We know that we can first divide the number 3 on both sides of the equation. We can then apply log on both sides because the way to pull down the x from an exponential is to use the logarithmic function. As the logarithm is the inverse of the exponential, they cancel each other and we can find the value of x.

Complete step by step answer:
We know that the given exponential to be solved is,
 \[3{{e}^{x}}=122\]
We can divide the number 3 on both sides, we get
\[\Rightarrow {{e}^{x}}=\dfrac{122}{3}\]
We know that the way to pull down the x from an exponential is to use the logarithmic function.
We can now apply log on both sides, we get
\[\Rightarrow \log {{\left( e \right)}^{x}}=\log \left( \dfrac{122}{3} \right)\]
We also know that as the logarithm is the inverse of the exponential, they cancel each other on the left-hand side, we get
\[\Rightarrow x=\log \left( \dfrac{122}{3} \right)\approx 3.7\]
We can use the scientific calculator to find the approximate value of the x.
Therefore, the value of \[x=\log \left( \dfrac{122}{3} \right)\approx 3.7\].

Note:
Students make mistakes while applying log on both sides, we should always remember that the logarithm is the inverse of the exponential, they cancel each other and the way to pull down the x from an exponential is to use the logarithmic function. We can also use the scientific calculator to find the approximate value of the x.