Question

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

Answer 1

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`