Question

Va rog mult ajutati-ma! :(

Answer 1

a)$27^x \geq 81 \\ 3^3^x \geq 3^4 \\ 3x \geq 4 \\ x \geq \frac{4}{3} \\ S=( \frac{4}{3}$;∞)
b)$5^x\ \textless \ 0,04 \\ 5^x\ \textless \ \frac{4}{100} \\ 5^x\ \textless \ \frac{1}{25} \\ 5^x\ \textless \ 25^-^1 \\ 5^x\ \textless \ 5^-^2 \\ x\ \textless \ -2$
c)$(\frac{5}{22} )^2^x^-^3 \leq 4,4 \\ (\frac{5}{22} )^2^x^-^3 \leq \frac{44}{10} \\ (\frac{5}{22} )^2^x^-^3 \leq \frac{22}{5} \\ (\frac{5}{22} )^2^x^-^3 \leq (\frac{5}{22} )^-^1 \\ 2x-3 \geq -1 \\ 2x \geq -1+3 \\ x \geq \frac{2}{2} \\ x \geq 1$
d)$(0,2)^3 \geq 125^4^-^3^x \\ (\frac{2}{10} )^3 \geq (5^3)^4^-^3^x \\ (\frac{1}{5}) ^3 \geq 5^1^2^-^9^x\\5^-^3 \geq 5^1^2^-^9^x \\ -3 \geq 12-9x \\ -9x \leq -12-3 \\ x \geq \frac{15}{9} \\x \geq \frac{5}{3}$
e)$(2,5)^-^4^x \geq (\frac{5}{2} )^4\\(2,5)^-^4^x \geq (2,5)^4\\-4x \geq 4\\x \leq -1$
f)$2^3^x^-^ x^{2} \geq 64^ \frac{1}{3} \\2^3^x^-^ x^{2} \geq 2^ \frac{6}{3} \\2^3^x^-^ x^{2} \geq 2^2\\3x-x^2 \geq 2\\-x^2+3x-2 \geq 0\\ x_{1}=2; x_{2}=1$
x∈[1;2]
g)$(0,01)^3^x\ \textless \ \sqrt{10} \\ (\frac{1}{100}) ^3^x\ \textless \ 10^ \frac{1}{2} \\10^-^6^x\ \textless \ 10^ \frac{1}{2} \\ -6x\ \textless \ \frac{1}{2} \\x\ \textgreater \ -\frac{1}{12}$