Question

Solve 7.8e^((x/3)ln(5))=14. What are the exact and approximate solutions?

Answer 1

Answer: a.

Step-by-step explanation: took the test and got i right

Answer 2

`\bold{\text{Answer}:\quad x=3\bigg((ln(14)/(7.8))/(ln(5))\bigg)=1.09}`

Explanation:

`7.8e^{(x)/(3)\cdot ln(5)}=14\\\\\\e^{(x)/(3)\cdot ln(5)}=(14)/(7.8)\\\\\\ln\bigg(e^{(x)/(3)\cdot ln(5)}\bigg)=ln\bigg((14)/(7.8)\bigg)\\\\\\(x)/(3)}\cdot ln(5)=ln\bigg((14)/(7.8)\bigg)\\\\\\\large\boxed{x=3\bigg((ln(14)/(7.8))/(ln(5))\bigg)}\\`

x ≈ 1.09