Question

(x)=3log(x+5)+2 what is the x intercept

Answer 1

`\large\boxed{x-intercept=-2+\sqrt[3]{0.01}}`

Explanation:

`f(x)=3\log(x+5)+2\to y=3\log(x+5)+2\\\\\text{Domain:}\ x+5>0\to x>-5\\\\\text{x-intercept is for }\ y=0:\\\\3\log(x+5)+2=0\qquad\text{subtract 2 from both sides}\\\\3\log(x+5)=-2\qquad\text{divide both sides by 3}\\\\\log(x+5)=-(2)/(3)\qquad\text{use the de}\text{finition of logarithm}\\\\(\log_ab=c\iff b^c=a),\ \log x=\log_(10)x\\\\\log(x+2)=-(2)/(3)\\\\\log_(10)(x+2)=-(2)/(3)\iff x+2=10^{-(2)/(3)}\qquad\text{use}\ a^(-n)=\left((1)/(a)\right)^n`

`x+2=\left((1)/(10)\right)^(2)/(3)\qquad\text{use}\ \sqrt[n]{a^m}=a^(m)/(n)\\\\x+2=\sqrt[3]{0.1^2}\qquad\text{subtract 2 from both sides}\\\\x=-2+\sqrt[3]{0.01}\in D`