[tex]y=\log(3x+4)+2\\\\Domain:3x+4 > 0\to x > -\dfrac{4}{3}\\\\x-intercept\ for\ y=0:\\\\\log(3x+4)+2=0\qquad|-2\\\\\log(3x+4)=-2\iff3x+4=10^{-2}\\\\3x+4=\dfrac{1}{10^2}\\\\3x+4=\dfrac{1}{100}\\\\3x+4=0.01\qquad|-4\\\\3x=-3.99\qquad|:3\\\\x=-1.33\in D\\----------------------------\\y-intercept\ for\ x=0\in D:\\\\y=\log(3(0)+4)\\\\y=\log(0+4)\\\\y=\log4\\\\y\approx0.60\\------------------------------\\\\Answer:\\x-intercept=\boxed{-1.33}\\\\y-intercept=\boxed{0.60}[/tex]
