Question

What are the exact and approximate solutions? (Picture below)

Answer 1

Answer: Option a.

Step-by-step explanation:

- Divide both sides of the expression by 7.8:

$7.8e^{\frac{x}{3}ln5}=14\\\\\frac{7.8e^{\frac{x}{3}ln5}}{7.8}=\frac{14}{7.8}\\\\e^{\frac{x}{3}ln5}=\frac{14}{7.8}$

- By definition:

$e^y=x$→$y=ln(x)$

Then:

$\frac{x}{3}ln5=ln(\frac{14}{7.8})$

- Now, you must solve for x.

Then, you obtain:

$xln5=3ln(\frac{14}{7.8})$

$x=\frac{3ln(\frac{14}{7.8})}{ln5}$≈$1.0903$