a)

$6^x=216$

$6^x=6^3$

zatem:

$x=3$    

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b) 

${0,4}^x=0,16$

${0,4}^x={0,4}^2$

zatem:

$x=2$    

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c)

${\left(2\frac{1}{3}\right)}^x=0$

równanie sprzeczne 

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d)

${\left(\frac{3}{4}\right)}^x=\frac{4}{3}$

${\left(\frac{3}{4}\right)}^x={\left(\frac{3}{4}\right)}^{-1}$

zatem:

$x=-1$    

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e)

${\left(\frac{3}{8}\right)}^x=18\frac{26}{27}$

${\left(\frac{3}{8}\right)}^x=\frac{512}{27}$

${\left(\frac{3}{8}\right)}^x={\left(\frac{8}{3}\right)}^3$

${\left(\frac{3}{8}\right)}^x={\left(\frac{3}{8}\right)}^{-3}$

zatem:

$x=-3$      

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f)

$\sqrt{{75}^x}=1$  

${75}^{\frac{x}{2}}={75}^0$

zatem:

$\frac{x}{2}=0$

$x=0$