Find a so that the graph of f(x) = log_a (x) contains the point (1/2, -4).
NOTE: log_a (x) = "log sub a x"
Let $\displaystyle y=\log _a x$
$\displaystyle (x, y) \implies \left(\frac12, -4\right) \implies x=\frac12, y=-4$
$\displaystyle \therefore -4 = \log _a \left(\frac12\right)$
The general rule to simplify this is: $\displaystyle \log _a n = x \implies a^x = n$
$\displaystyle \therefore -4 = \log _a \left(\frac12\right) \implies a^{-4} = \frac12$
$\displaystyle \therefore a = \sqrt[-4] {\frac12} = \left(\frac12\right)^{-\frac14}$
$\displaystyle \therefore a = (2)^{\frac14} = \sqrt[4]2 \approx 1.19\text{ to 3 s.f}$