Question

enter the correct values in the boxes.
show hints
$e^{0.26x} + 26 = 326$
$e^{0.26x} = \square$
$0.26x = \ln(\square)$
$x \approx \square$

Explanation:

Step1: Isolate the exponential term

Subtract 26 from both sides of the equation \( e^{0.26x} + 26 = 326 \).
\( e^{0.26x} = 326 - 26 = 300 \)

Step2: Take the natural logarithm

Take the natural logarithm of both sides to solve for the exponent. Since \( \ln(e^y) = y \), we have:
\( 0.26x = \ln(300) \)

Step3: Solve for x

Divide both sides by 0.26 to find x. First, calculate \( \ln(300) \approx 5.70378 \). Then:
\( x = \frac{\ln(300)}{0.26} \approx \frac{5.70378}{0.26} \approx 21.9376 \)

Answer:

First box: 300
Second box: 300
Third box: 21.94 (or a more precise decimal like 21.9376)