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

Rishi Hale
2022-07-18
Answered

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

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renegadeo41u

Answered 2022-07-19
Author has **9** answers

Hint:

$y={\mathrm{log}}_{b}x,-3={\mathrm{log}}_{b}\frac{1}{8},b=2$

$f(x)={\mathrm{log}}_{2}x,{f}^{-1}(x)={2}^{x},{f}^{-1}(4)=?$

$y={\mathrm{log}}_{b}x,-3={\mathrm{log}}_{b}\frac{1}{8},b=2$

$f(x)={\mathrm{log}}_{2}x,{f}^{-1}(x)={2}^{x},{f}^{-1}(4)=?$

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b) ${\mathrm{log}}_{5}(2x)+{\mathrm{log}}_{5}(4x)=2\phantom{\rule{0ex}{0ex}}x=?$

a) $\mathrm{ln}(5x)=0\phantom{\rule{0ex}{0ex}}x=?$

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