Question

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

Answer 1

$\bold{\text{Answer}:\quad x=3\bigg(\dfrac{ln\frac{14}{7.8}}{ln(5)}\bigg)=1.09}$

Step-by-step explanation:

$7.8e^{\frac{x}{3}\cdot ln(5)}=14\\\\\\e^{\frac{x}{3}\cdot ln(5)}=\dfrac{14}{7.8}\\\\\\ln\bigg(e^{\frac{x}{3}\cdot ln(5)}\bigg)=ln\bigg(\dfrac{14}{7.8}\bigg)\\\\\\\frac{x}{3}}\cdot ln(5)=ln\bigg(\dfrac{14}{7.8}\bigg)\\\\\\\large\boxed{x=3\bigg(\dfrac{ln\frac{14}{7.8}}{ln(5)}\bigg)}$

x ≈ 1.09