a)

${0,75}^{x+5}={\left(1\frac{1}{3}\right)}^{x+1}$  

${\left(\frac{3}{4}\right)}^{x+5}={\left(\frac{4}{3}\right)}^{x+1}$

${\left(\frac{3}{4}\right)}^{x+5}={\left(\frac{3}{4}\right)}^{-\left(x+1\right)}$

zatem:

$x+5=-\left(x+1\right)$

$x+5=-x-1$

$2x=-6\mid :2$

$x=-3$       

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b) 

${\left(6\frac{1}{4}\right)}^{2x-1}={0,4}^{3x-12}$

${\left(\frac{25}{4}\right)}^{2x-1}={\left(\frac{2}{5}\right)}^{3x-12}$  

${\left({\left(\frac{5}{2}\right)}^2\right)}^{2x-1}={\left(\frac{5}{2}\right)}^{-\left(3x-12\right)}$

${\left(\frac{5}{2}\right)}^{4x-2}={\left(\frac{5}{2}\right)}^{-3x+12}$    

zatem:

$4x-2=-3x+12$

$7x=14\mid :7$

$x=2$    

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c)

${\left(1\frac{1}{6}\right)}^{2x-4}-{\left(\frac{6}{7}\right)}^{x+2}=0$

${\left(\frac{7}{6}\right)}^{2x-4}={\left(\frac{6}{7}\right)}^{x+2}$

${\left(\frac{7}{6}\right)}^{2x-4}={\left(\frac{7}{6}\right)}^{-\left(x+2\right)}$

zatem:

$2x-4=-x-2$

$3x=2\mid :3$

$x=\frac{2}{3}$        

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d)

${0,5}^{3x-4}=8^{2x+1}$

${\left(\frac{1}{2}\right)}^{3x-4}={\left(2^3\right)}^{2x+1}$

$2^{-\left(3x-4\right)}=2^{6x+3}$

zatem:

$-\left(3x-4\right)=6x+3$

$-3x+4=6x+3$

$-9x=-1\mid :\left(-9\right)$

$x=\frac{1}{9}$        

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e)

${\left(\frac{1}{4}\right)}^{x^2}-8^{-x}=0$

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

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

zatem:

$2x^2=3x$

$2x^2-3x=0$

$x\left(2x-3\right)=0$

$x=0\text{lub}2x-3=0$

$x=\frac{3}{2}$          

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f)

$5^{\frac{2}{x-1}}={0,04}^3,x\ne 1$  

$5^{\frac{2}{x-1}}={\left(\frac{1}{25}\right)}^3$

$5^{\frac{2}{x-1}}={\left({\left(\frac{1}{5}\right)}^2\right)}^3$

$5^{2/\left(x-1\right)}=5^{-6}$

zatem:

$\frac{2}{x-1}=-6$

$-6x+6=2$

$-6x=-4\mid :\left(-6\right)$

$x=\frac{4}{6}=\frac{2}{3}$