Sure! Let's solve the equation step by step.
Given the equation:
[tex]\[ 6 \cdot e^x = 25 \][/tex]
Step 1: Isolate the exponential term.
To do this, divide both sides of the equation by 6:
[tex]\[ e^x = \frac{25}{6} \][/tex]
Step 2: Simplify the fraction.
[tex]\[ \frac{25}{6} \approx 4.16667 \][/tex]
Step 3: Solve for [tex]\( x \)[/tex].
Take the natural logarithm (ln) of both sides to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \ln\left(\frac{25}{6}\right) \][/tex]
Step 4: Calculate the natural logarithm value.
[tex]\[ x \approx \ln(4.16667) \][/tex]
Step 5: Using a calculator to find the natural logarithm of 4.16667:
[tex]\[ x \approx 1.4271163556401458 \][/tex]
Step 6: Round the result to two decimal places.
[tex]\[ x \approx 1.43 \][/tex]
Therefore, the solution to the equation [tex]\( 6 \cdot e^x = 25 \)[/tex] rounded to two decimal places is:
[tex]\[ \boxed{1.43} \][/tex]
So, the correct answer is:
C. [tex]\( x = 1.43 \)[/tex]
