Answer: [tex]\frac{1}{e^{\frac{2}{3}}}+5[/tex] or 5.51
Step-by-step explanation:
The given function : [tex]f(x)= 3\log(x-5)+2[/tex]
We know that , the x-intercept is the point on graph( basically intersection of graph and x-axis) where y coordinate is zero.
I.e. for x-intercept of function , f(x) =0
i.e. [tex]0= 3\log(x-5)+2[/tex]
[tex]\Rightarrow\ \log(x-5)=\dfrac{-2}{3}[/tex]
Taking exponent on both sides , we get
[tex]x-5=e^{\frac{-2}{3}}\\\\\Rightarrow\ x=e^{\frac{-2}{3}}+5\ \ or\ \ x=\dfrac{1}{e^{\frac{2}{3}}}+5[/tex]
On simplification , [tex]\frac{1}{e^{\frac{2}{3}}}+5\approx5.51[/tex].
Hence , the x-intercept of the graph f(x)= [tex]\dfrac{1}{e^{\frac{2}{3}}}+5[/tex] or 5.51.
