Question

The x-intercept of the graph of f(x)= 3log(x-5)+2 is:

Answer 1

Your answers we equal to 22

Answer 2

Answer: $\frac{1}{e^{\frac{2}{3}}}+5$ or 5.51

Step-by-step explanation:

The given function : $f(x)= 3\log(x-5)+2$

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. $0= 3\log(x-5)+2$

$\Rightarrow\ \log(x-5)=\dfrac{-2}{3}$

Taking exponent on both sides , we get

$x-5=e^{\frac{-2}{3}}\\\\\Rightarrow\ x=e^{\frac{-2}{3}}+5\ \ or\ \ x=\dfrac{1}{e^{\frac{2}{3}}}+5$

On simplification , $\frac{1}{e^{\frac{2}{3}}}+5\approx5.51$.

Hence , the x-intercept of the graph f(x)=      $\dfrac{1}{e^{\frac{2}{3}}}+5$ or 5.51.