Answer: Option a.
Step-by-step explanation:
- Divide both sides of the expression by 7.8:
[tex]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}[/tex]
- By definition:
[tex]e^y=x[/tex]→[tex]y=ln(x)[/tex]
Then:
[tex]\frac{x}{3}ln5=ln(\frac{14}{7.8})[/tex]
- Now, you must solve for x.
Then, you obtain:
[tex]xln5=3ln(\frac{14}{7.8})[/tex]
[tex]x=\frac{3ln(\frac{14}{7.8})}{ln5}[/tex]≈[tex]1.0903[/tex]
