The graph of \( f(x)=\log _{4} x \) is drawn below \( \mathrm{B}(k ; 2) \) is a point on \( f \).

In the context of the function \( f(x) = \log_4 x \), point \( B(k; 2) \) means that when \( f(k) = 2 \). To find \( k \), we can use the definition of the logarithm: \( f(k) = 2 \) translates to \( k = 4^2 = 16 \). Hence, \( B(16; 2) \) is a point on the graph of the function, showing that \( x = 16 \) yields a logarithmic value of 2. If you want to see how logarithmic functions apply in real life, consider their utility in measuring the intensity of earthquakes with the Richter scale. Each whole number increase in the Richter scale corresponds to a ten-fold increase in measured amplitude and roughly 31.6 times more energy release! Logarithms help us manage these vast differences in scale, making complex data easier to understand.