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

Question

asked Apr 16, 2020 199k views

1 Answer

Paul Stanley · Answer 1 · 2020-04-23T09:27:26+0000

Answer: Option a.

Explanation:

- Divide both sides of the expression by 7.8:

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

- By definition:

e^y=x →
y=ln(x)

Then:

(x)/(3)ln5=ln((14)/(7.8))

- Now, you must solve for x.

Then, you obtain:

xln5=3ln((14)/(7.8))

x=(3ln((14)/(7.8)))/(ln5) ≈
1.0903