Find the Asymptotes y=3* log of x+7-4

Find where the expression ${\displaystyle 3\cdot \log (x+7)-4}$ is undefined.

Since ${\displaystyle 3\cdot \log (x+7)-4}$${\displaystyle \to }$${\displaystyle \infty }$ as ${\displaystyle x}$${\displaystyle \to }$${\displaystyle -7}$ from the left and ${\displaystyle 3\cdot \log (x+7)-4}$${\displaystyle \to }$${\displaystyle -\infty }$ as ${\displaystyle x}$${\displaystyle \to }$${\displaystyle -7}$ from the right, then ${\displaystyle x=-7}$ is a vertical asymptote.

Ignoring the logarithm, consider the rational function ${\displaystyle R\left(x\right)=\frac{a{x}^n}{b{x}^m}}$ where ${\displaystyle n}$ is the degree of the numerator and ${\displaystyle m}$ is the degree of the denominator.

There are no horizontal asymptotes because ${\displaystyle Q\left(x\right)}$ is ${\displaystyle 1}$.

No oblique asymptotes are present for logarithmic and trigonometric functions.

This is the set of all asymptotes.