3. Solve the inequality $5^{\frac{x+5}{x+4}} \cdot 3^{x+4} \geq 75$.
Answer: $x \in(-4 ;-3] \cup\left[\log _{3} 5-4 ;+\infty\right)$.

Solution. Taking the logarithm of both sides of the inequality with base 3, we get:

$$
\frac{x+5}{x+4} \log _{3} 5+(x+4) \geq 1+2 \log _{3} 5 \Leftrightarrow \frac{-x-3}{x+4} \log _{3} 5+(x+3) \geq 0 \Leftrightarrow \frac{(x+3)\left(-\log _{3} 5+x+4\right)}{x+4} \geq 0
$$

Solving the last inequality using the interval method, we find that $x \in(-4 ;-3] \cup\left[\log _{3} 5-4 ;+\infty\right)$.