Question

question 4 of 10
what is the solution to the equation below? round your answer to two decimal places.
( e^x = 0.7 )

a. ( x = 2.01 )
b. ( x = -0.36 )
c. ( x = 5.01 )
d. ( x = -0.15 )

Explanation:

Step1: Take natural log of both sides

To solve \( e^{x}=0.7 \), we take the natural logarithm (ln) of both sides. Recall that \( \ln(e^{x}) = x \) because the natural logarithm and the exponential function (with base \( e \)) are inverse functions. So, applying \( \ln \) to both sides gives:

$$ \ln(e^{x})=\ln(0.7) $$

Simplifying the left - hand side, we get \( x = \ln(0.7) \).

Step2: Calculate the value of \( \ln(0.7) \)

Using a calculator, we know that the natural logarithm of 0.7. We can calculate \( \ln(0.7)\approx - 0.3566749439\).

Step3: Round to two decimal places

Rounding \( - 0.3566749439\) to two decimal places, we look at the third decimal place which is 6. Since \( 6\gt5 \), we round up the second decimal place. So, \( - 0.3566749439\approx - 0.36\).

Answer:

B. \( x = - 0.36 \)