[tex]y=log(3x+4)+2[/tex]
To find the x-intercept we make the value of y=0, then,
[tex]0=log(3x+4)+2[/tex]
clear the equation for x
[tex]\begin{gathered} -2=log(3x+4) \\ write\text{ }the\text{ }equation\text{ }in\text{ }exponential\text{ }form \\ 10^{-2}=3x+4 \\ \frac{1}{10^2}=3x+4 \\ solve\text{ }for\text{ }x \\ \frac{1}{100}=3x+4 \\ \\ \frac{1}{100}-4=3x \\ \\ -\frac{399}{100}=3x \\ \\ x=-\frac{399}{100}\times\frac{1}{3} \\ \\ x=-\frac{133}{100}=-1.33 \end{gathered}[/tex]
The x-intercept is -1.33
To find the y-intercept we make the value of x=0, then,
[tex]\begin{gathered} y=log(3(0)+4)+2 \\ y=log(4)+3 \\ using\text{ }exponential\text{ }form \\ y=log(2^2)+2 \\ y=2log(2)+2 \\ y\cong2.602 \end{gathered}[/tex]
Answer:
The intercepts are:
y-intercept is y=2.602
x-intercept is x=-1.33
