Question 1103292
{{{L=k/x^2+L[ambient]}}}
Substituting {{{L[ambient]=239}}}
and the coordinates {{{system(x=10,L=2513)}}} of our data point,
{{{2513=k/10^2+239}}}
{{{2513-239=k/100}}}
{{{2274=k/100}}}
{{{2274*100=k}}}
{{{k=227400}}}
{{{highlight(L=227400/x^2+239)}}}
To get {{{L=1400}}} ,
{{{1400=227400/x^2+239)}}}
means
{{{1400-239=227400/x^2}}}
{{{1161=227400/x^2}}}
{{{1161x^2=227400}}}
{{{x^2=227400/1161=75800/387=100*758/(9*43)}}}
There are two solutions to that equation,
but we are looking for a positive distance, so
{{{x=sqrt(227400/1161)=sqrt(75800/758)}}}
At this point, you could just reach for the calculator,
because it does not simplify much.
The approximate answer from the calculator is
{{{x=13.9952}}} ,
so we should place the light at {{{highlight(14cm)}}} from whatever point we want with 1400 lux of light intensity.