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.