Question

question 7 of 10
what is the solution to the equation below? round your answer to two decimal places.
ln x = 0.2

a. x = -0.70
b. x = -1.61
c. x = 1.58
d. x = 1.22

Explanation:

Step1: Recall the inverse of natural log

The natural logarithm function $\ln x$ has an inverse function $e^x$. To solve $\ln x = 0.2$, we exponentiate both sides with base $e$.
$$e^{\ln x}=e^{0.2}$$

Step2: Simplify using inverse property

Using the property $e^{\ln a}=a$ for $a>0$, the left side simplifies to $x$. So we need to calculate $e^{0.2}$.
Using a calculator, $e^{0.2}\approx1.221402758$.

Step3: Round to two decimal places

Rounding $1.221402758$ to two decimal places gives $1.22$.

Answer:

D. $x = 1.22$