A child is 20 inches long at birth. If we consider that the baby will grow at a rate proportional to its body size until adulthood, then the percentage of her adult height attained can be modeled by the logarithmic function
\[
f(x)=20+47 \log (x+2)
\]
where $x$ represents her age in years and $f(x)$ represents the percentage of her adult helght reached at age $x$. What percent of the child's adult height is attained by age 6 ? Round your answer to the nearest whole percentage, If necessary.

Step 1 ：We are given a child's growth function as \(f(x)=20+47 \log (x+2)\), where \(x\) represents her age in years and \(f(x)\) represents the percentage of her adult height reached at age \(x\).

Step 2 ：We are asked to find the percentage of the child's adult height attained by age 6. This can be found by substituting \(x=6\) into the given function.

Step 3 ：Substituting \(x=6\) into the function, we get \(f(6)=20+47 \log (6+2)\).

Step 4 ：Calculating the above expression, we get \(f(6) = 117.73375245895228\).

Step 5 ：Rounding this to the nearest whole number, we get \(118\).

Step 6 ：So, the child will have attained \(\boxed{118\%}\) of her adult height by age 6.