# A point on a graph is (1/8,−3) of the logarithmic function f(x)=log b^x, and the point (4,k) is on the graph of the inverse, y=f^(-1)(x).Determine the value k.

A point on a graph is (1/8,−3) of the logarithmic function $f\left(x\right)=\mathrm{log}{b}^{x}$, and the point (4,k) is on the graph of the inverse, $y={f}^{-1}\left(x\right)$. Determine the value k.
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Hint:
$y={\mathrm{log}}_{b}x,-3={\mathrm{log}}_{b}\frac{1}{8},b=2$
$f\left(x\right)={\mathrm{log}}_{2}x,{f}^{-1}\left(x\right)={2}^{x},{f}^{-1}\left(4\right)=?$