To solve the equation [tex]\(e^{0.3x} = 0.3\)[/tex], we need to isolate [tex]\(x\)[/tex]. Here’s the step-by-step solution:
1. Rewrite the equation in logarithmic form to isolate the exponent:
[tex]\[
e^{0.3x} = 0.3
\][/tex]
Taking the natural logarithm (ln) on both sides gives:
[tex]\[
\ln(e^{0.3x}) = \ln(0.3)
\][/tex]
2. Simplify the left side:
Note that [tex]\(\ln(e^y) = y\)[/tex], so:
[tex]\[
0.3x = \ln(0.3)
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], divide both sides by 0.3:
[tex]\[
x = \frac{\ln(0.3)}{0.3}
\][/tex]
4. Calculate [tex]\(\ln(0.3)\)[/tex]:
The natural logarithm of 0.3 is approximately [tex]\(-1.2039728043259361\)[/tex].
5. Divide by 0.3:
[tex]\[
x = \frac{-1.2039728043259361}{0.3} \approx -4.013242681086454
\][/tex]
6. Round to two decimal places:
[tex]\[
x \approx -4.01
\][/tex]
So, the solution to the equation [tex]\(e^{0.3x} = 0.3\)[/tex], rounded to two decimal places, is:
[tex]\[
\boxed{-4.01}
\][/tex]
Therefore, the correct answer is:
B. [tex]\(x = -4.01\)[/tex]
