Logarifmik tengsizliklar mavzusidan test savollari

Tengsizlikni yeching. \log _{\frac{1}{3}}(x^{2}-2x+3)-\log _{\frac{1}{3}}6>0

Tengsizlikni yeching:

\log _{2}(x^{2}-5x+4)<2

Tengsizlikni yeching:

\log _{2}(x^{2}-9x+8)<3

Tengsizlikni yeching:

\log _{3}(x^{2}-2x)\le 1

Tengsizlikni yeching:

\log _{2}(\log _{3}(\frac{x-3}{2}))<0

Tengsizlikni yeching:

\log _{4}(x^{2}-10x+16)<2

Nechta butun son \log _{3}(x^{2}-8x)\le 2 tengsizlikni qanoatlantiradi.

Tengsizlikning butun yechimlari nechta?

\frac{(x-\frac{1}{2})\cdot (3-x)}{\log _{2}|x-1|}>0

Tengsizlikni yeching:

\log _{3}(x-5)<3

\vert 1-\log _{\frac{1}{3}}(x-2)\vert<3 tengsizlikni qanoatlantiruvchi nechta butun son bor?

3^{\log _{3}(7-x)}\le 2 tengsizlikni yeching.

Tengsizlikni yeching:

\frac{1+\log _{2}x}{1-\log _{4}x}\le 2

Tengsizlikni yeching:

\log _{x-2}(x^{2}-3)>0

Tengsizlikni yeching:

\log _{\frac{1}{\sqrt{3}}}(x-9)+2\log _{\sqrt{3}}(x-9)<4

Tengsizlikni qanoatlantiruvchi nechta butun son mavjud?

7^{\log _{7}(x^{2}-3x)}<4

Nechta butun son \log_{2}(x^{2}-7x)<3 tensizlikni qanoatlantiradi?

\log _{\frac{2}{3}}\frac{x}{4}\le \log _{\frac{4}{9}}(x-3) tengsizlikni yeching.

\log _{3}(x^{2}-2x)\le 1 tengsizlik nechta butun yechimga ega?

Tengsizlikni yeching:

\log _{\frac{1}{5}}(x^{2}-2x+4)-\log _{\frac{1}{5}}19>0

Tengsizlikni yeching:

\log _{x-1}(x^{2}-x+1)\ge 2

Tengsizlikni yeching:

\frac{1-\log _{5}x}{1+\log _{5}x}\ge \frac{1}{3}

\vert x-8\vert (\log _{5}(x^{2}-3x-4)+\frac{2}{\log _{3}0.2})\le 0 tengsizlik yechimlarining nechtasi butun sondan iborat?

Tengsizlikni yeching:

\log _{x}2\cdot \log _{\frac{x}{16}}2>\frac{1}{\log _{2}x-6}

Tengsizlikni yeching:

\log _{\frac{1}{3}}(x^{2}-2x)\ge -1

Tengsizlikni yeching:

(\frac{\pi }{2}-\frac{e}{3})^{\ln (2cosx)}\ge 1 (x\in0;2\pi )

\log _{x^{2}-x}(3x^{2}-6x-3)=1 tenglama ildizlarining yig‘indisini toping.

Tengsizlikni yeching:

\log _{5}(x+1)+\log _{5}(x-1)\le 3

Tengsizlikni yeching:

\log _{0.5}(x^{2}-4)<\log _{0.5}3x

Quyidagi tengsizlikning barcha butun sonlardan iborat yechimlari yig‘indisini toping:

\sqrt{5-x}(\log _{\frac{1}{3}}(2x-4)+\frac{1}{\log _{x}3})\ge 0

\frac{5}{lg^{2}x-9}\ge \frac{1}{lgx-3} tengsizlikni yeching.