Wribreeminsl

2021-01-15

Solve the equation and find the exact solution:
$\mathrm{log}base2\left(\mathrm{log}base3\left(\mathrm{log}base4\left(x\right)\right)\right)=0$

dessinemoie

Expert

Start with $x={4}^{3}=64,$
$\mathrm{log}\left[4\right]\left(64\right)=3$,
$\mathrm{log}\left[3\right]\left(3\right)=1,$
$\mathrm{log}\left[2\right]\left(1\right)=0,$
so x=64 is a solution.
Another way: $\mathrm{log}\left[2\right]\left(z\right)=0$,
so z=1, $\mathrm{log}\left[3\right]\left(y\right)=1$,
so y=3, $\mathrm{log}\left[4\right]\left(x\right)=3$,
so $x={4}^{3}=64.$

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