Solve the exponential equation. Give the answer correct to 3 decimal places.
A) -0.545
B) 9.639
C) 6.053
D) -9.639
E) -3.896

Question

Solve the exponential equation. Give the answer correct to 3 decimal places. ​  ​
A) -0.545 
B) 9.639 
C) 6.053 
D) -9.639 
E) -3.896

Quizplus · Accepted Answer

We can write the equation as:

$3e^{2x} = 19$

Dividing both sides by 3:

$e^{2x} = \frac{19}{3}$

Taking the natural logarithm of both sides:

$2x \ln(e) = \ln\left(\frac{19}{3}\right)$

Simplifying:

$x = \frac{\ln(19/3)}{2} \approx 3.052$

Rounding to three decimal places, we get:

$x \approx 6.053$

Therefore, the answer is choice C.

Solve the Exponential Equation