Logarifmik tenglamalar mavzusidan test savollari

Tenglamani yeching (bu yerda a>0, a\ne1) \log_{a^{4}}x^{3}+\log_{a^{12}}x^{5}-\log_{a^{36}}x^{6}=2

Tenglamani yeching:

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

Tenglamani yeching (bu yerda a>0, a\ne 1)

\log_{a^{3}}x^{2}+\log_{a^{4}}x^{4}-\log_{a^{27}}x^{3}=1

\log_{x}27+\log_{3}x=4 tenglamaning ildizlari yig‘indisini toping.

\log_{x}(x^{2}+2x)=3 tenglama nechta ildizga ega?

\log_{5}9\cdot \log_{3}e\cdot ln25=\log_{x}16 bo‘lsa, x nechaga teng?

\log_{x}y+\log_{y}x=2 va x^{2}=3y+10 bo‘lsa, x+y=?

40\% qismi 10 ga teng son lgx=2 tenglama yechimining necha foizini tashkil etadi?

\log_{2}(x-4)+\log_{2}(x-1)=2 tenglama nechta ildizga ega?

Tenglamaning ildizlari yig‘indisini toping:

\log_{3}^{2}x-4\log_{3}x+3=0

\log_{3}x=3^{x} tenglama nechta ildizga ega?

|x-1|^{\log_{2}x-lgx^{2}}=|x-1|^{3} tenglama nechta yechimga ega?

\log_{2}\sqrt[3]{4\sqrt[3]{4\sqrt[3]{4\sqrt[3]{4_\cdots }}}}=?

Tenglamani yeching:

\log_{x}(\log_{x}256)=\log_{2}8

\log_{2}(x-2)-x^{2}+2x-3=0 tenglama nechta yechimga ega?

5^{x}+\log_{5}x=0 tenglama nechta ildizga ega?

lg(\frac{1}{\log_{2}x})+1=0 tenglamaning ildizini toping.

Tenglamaning ildizlari yig‘indisini toping:

\log_{4}(5x-6)\cdot \log_{x}256=8

Tengsizlikni yeching:

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

\log_{2\sqrt{3}}x+\log_{2\sqrt{3}}(x-1)=2 tenglamaning ildizlari yig‘indisini toping.

\log_{2\sqrt{3}}x+\log_{2\sqrt{3}}(x-1)=2 tenglamaning ildizlari yig‘indisini toping.

Tenglamaning ildizlari yig‘indisini toping:

\log_{x}3\cdot \log_{4}6\cdot \log_{5}4\cdot \log_{3}5\cdot \log_{6}(5x+6)=\log_{6}36

k ning qanday qiymatlarida (2014x-k)\cdot \log_{2014}(x-1)=0 tenglama bitta ildizga ega bo‘ladi?

y=\sqrt[5]{x^{2}-7x+10}+lg\vert x^{2}-5x+4\vert funksiyaning aniqlanish sohasini toping.

lg^{2}x^{2}-lg^{2}(-x)=27 tenglamani yeching.

Tenglamani yeching:

lg(0.5^{x})+lg(0.125^{x})+lg(0.03125^{x})=lg(0.25^{2})+lg(0.0625^{3}).

\log_{3}^{2}(x^{2}-7x+7)+\log_{4}^{2}(x^{2}-12x+12)=0 tenglama nechta ildizga ega?

Tenglamaning ildizlar yig‘indisini toping:

2(\lg\sqrt{x}-\lg2)=\lg(\sqrt{x}-1)

\log_{x}y+\log_{y}x=2 va x^{2}=3y+10 bo‘lsa, x+y=?