Степенные неравенства mavzusidan test savollari

Tenglamaning kata ildizini toping:
3^{5-2x^{2}}-4\cdot 3^{-x^{2}-5}=-3^{-14}

\begin{cases}3^{3x-1}+4^{y}=21 \\ -27^{2x}+2^{2y}=11 \end{cases} bo‘lsa, x ga teskari sonni toping.

\begin{cases}{3^{2x-y}=\sqrt[3]{27^{2}}} \\ {9^{x}\cdot 9^{y}=3^{14}} \end{cases} tenglamani qanoatlantiruvchi barcha x va y larning yig‘indisini toping.

\begin{cases}3^{m}+2\cdot 4^{n+1}=17 \\ 4^{n}-5\cdot 3^{m}=-44 \end{cases} bo‘lsa,

m+n=?

Tengsizlikni yeching:

(\frac{1}{3})^{x^{2}+2x}+(\frac{1}{3})^{x^{2}+2x-2}>\frac{10}{27}

(4^{\sqrt{x-6}}-1)(3\cdot 2^{x}-96)<0 tengsizlikni yeching.

(4^{\sqrt{x-6}}-1)(3\cdot 2^{x}-96)\ge 0 tengsizlikni qanoatlantiruvchi eng kichik natural sonni toping.

Tengsizlikni yeching:

(\sqrt{\pi }-1)^{\ln (2sinx)}\ge 1;x\in[0;2\pi ]

0.(3)^{12-5x}<27 tengsizlikning nechta natural yechimi mavjud

Tengsizlik x ning nechta butun qiymatida o‘rinli?

4\cdot (0.2)^{x^{2}+x-2}-15\cdot (0.2)^{x^{2}+x-1}\ge 1

Quyidagi tenglamaning ildizlari nisbatini toping:

(\sqrt{2+\sqrt{3}})^{x}+(\sqrt{2-\sqrt{3}})^{x}=4

25<3^{2x-3}<90 tensizlikni qanoatlantiruvchi nechta butun son mavjud?

Tengsizlikni yeching:

(\frac{1}{3})^{5-2x}\ge 27

(x+2)^{\log_{2}(x^{2}+1)}<(x+2)^{\log_{2}(2x+9)}

8<3^{2x-3}<90 tensizlikni qanoatlantiruvchi nechta butun son mavjud?

Tengsizlik x ning nechta butun qiymatida o‘rinli:

(0.5)^{x^{2}-x-4}-3\cdot (0.5)^{x^{2}-x-2}>1

30<3^{2x+5}<70 tensizlikni qanoatlantiruvchi nechta butun son mavjud?

Tengsizlikni yeching:

(\frac{\pi }{2}-\frac{e}{3})^{\ln (2cosx)}\ge 1 x\in[0;2\pi ]

Tengsizlikni yeching (\frac{4}{5})^{\sin ^{2}x}\cdot (\frac{25}{16})^{cosx}<2^{2}\cdot 5^{-1}

Quyidagi tenglama nechta ildizga ega?

3^{x}=x^{2}+3

Tengsizlik x ning nechta butun qiymatida o‘rinli?

2^{x^{2}-x-6}+3\cdot 2^{x^{2}-x-4}>13

(x-2)^{x^{2}-6}>(x-2)^{10} tengsizlikni yeching.

Quyidagi sonlardan qaysilari birdan kata?

1) 0.2^{x}\cdot 5^{y}x>1 va y<0;

2) 0.75^{x}\cdot 1.(3)^{y}x<0 va y>0;

3) 0.4^{x}\cdot 2.5^{y}x>y>0;

4) 0.(3)^{x}\cdot 3^{y}x<y<0;

5) 0.8^{x}\cdot 1.25^{x}x>1

18<5^{x-2}<4012 tengsizlikni qanoatlantiruvchi butun sonlar yig‘indisini toping.

Quyidagi tengsizlik nechta natural ildizga ega?

(\frac{25}{49})^{x-10}\ge (\frac{7}{5})^{2x-10}