Zad. 1
a)
2^{x+3}+2^x=72
2^x*2^3+2^x=72
2^x=t t>0
8t+t=72
9t=72/:9
t=8
2^x=8
x=3, bo 2^3=8
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b)
8*3^{x-2}+9^{x-1}=17
8*3^x*3^{-2}+9^x*9^{-1}=17
8*3^x*\frac{1}9+3^{2x}*\frac{1}{9}=17
\frac{8}{9}*3^x+\frac{1}{9}*3^{2x}=17/*9
3^x=t, t>0
8t+t^2-153=0
t^2+8t-153=0
\Delta=64+612=676
\sqrt{\Delta}=26
$x_1=\frac{-8-26}{2}=-17$nie spełnia warunków zadania
x_2=\frac{-8+26}{2}=9
3^x=9
x=2,odp
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