Rozwiąż nierówność:
1.
2.
3*3^x+3^x≤ 4/9
4*3^x≤4/9 /:4
3^x≤3^(-2)
x≤-2
2. 1/5*9/25 * (5/3)^x - 3/25*(5/3)^2x≥0
t= (5/3)^x , t > 0
3/25 t²- 9/125t≥0 /. 125
15t²-9t≥0
3t(5t-3)≥0
5t-3≥0
t≥3/5
(5/3)^x≥3/5
(3/5)^-x≥3/5
-x≤1
x≥-1
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3*3^x+3^x≤ 4/9
4*3^x≤4/9 /:4
3^x≤3^(-2)
x≤-2
2. 1/5*9/25 * (5/3)^x - 3/25*(5/3)^2x≥0
t= (5/3)^x , t > 0
3/25 t²- 9/125t≥0 /. 125
15t²-9t≥0
3t(5t-3)≥0
5t-3≥0
t≥3/5
(5/3)^x≥3/5
(3/5)^-x≥3/5
-x≤1
x≥-1