c)
(\frac{2}{3})^x+(\frac{2}{3})^{x-3}\leq \frac{35}{27}
(\frac{2}{3})^x+(\frac{2}{3})^{x}*(\frac{2}{3})^{-3}\leq \frac{35}{27}
(\frac{2}{3})^x+(\frac{2}{3})^x+(\frac{3}{2})^3\leq \frac{35}{27} |(2/3)^x wyłączam przed nawias:
(\frac{2}{3})^x(1+\frac{27}{8})\leq \frac{35}{27}
(\frac{2}{3})^x*\frac{8+27}{8}\leq \frac{35}{27}
(\frac{2}{3})^x*\frac{35}{8}\leq \frac{35}{27} --------|:\frac{35}{8}
(\frac{2}{3})^x\leq \frac{35}{27}*\frac{8}{35}
(\frac{2}{3})^x\leq \frac{8}{27}
(\frac{2}{3})^x\leq (\frac{2}{3})^3 |zmieniamy znak nierówności na przeciwny, bo \frac{2}{3}<1
x\geq 3
x\in \langle 3;+\infty)
d)
2*5^x-5^{x-1}< 9
2*5^x-5^{x}*5^{-1}< 9
2*5^x-5^x*\frac{1}{5}<9
5^x(2-\frac{1}{5})<9
5^x*\frac{10-1}{5}<9
5^x*\frac{9}{5}<9 |:9
5^x*\frac{1}{5}<1 |*5
5^x<5^1
x<1
x\in (-\infty;1)