Given that \(a\) and \(b\) are positive and \[4(\log_{10}a)^2+(\log_{10}b)^2=1\] then the greatest possible value of \(a\) is

\(\frac{1}{10}\),

\(1\),

\(\sqrt{10}\),

\(10^{\sqrt{2}}\).

Given that \(a\) and \(b\) are positive and \[4(\log_{10}a)^2+(\log_{10}b)^2=1\] then the greatest possible value of \(a\) is

\(\frac{1}{10}\),

\(1\),

\(\sqrt{10}\),

\(10^{\sqrt{2}}\).