bpt logarit đưa về cùng cơ số :

1, \(2lg\left[\left(x-1\right)\sqrt{5}\right]>lg\left(x-5\right)+1\)

2, \(log_{\dfrac{1}{2}}\left[log_2\left(3^x+1\right)\right]>-1\)

3, \(log_x\dfrac{3x-1}{x^2+1}>0\)

4, \(\left(0,08\right)^{log_{x-0,5}x}\ge\left(\dfrac{5\sqrt{2}}{2}\right)^{log_{x-0,5}\left(2x-1\right)}\)

Tìm TXĐ:

a) y=\(\left(1-x\right)^{\dfrac{-1}{3}}\)

b) \(y=\sqrt{\log_{0,5}\dfrac{2x+1}{x+5}-2}\)

c) \(y=\log_{10}\sqrt{x^2-x-12}\)

d) \(y=\sqrt{\log_{10}x-1+\log_{10}x+1}\)

1.rút gọn A=3\(\log_4\sqrt{a}\)- \(\log_{\dfrac{1}{2}}a^2\)+ 2\(\log_{\sqrt{2}}a\)

2.bt \(\log_23=a\). tính \(\log_{12}36\) theo a

tính

a) \(log_{\sqrt{2}}\sqrt{2};log_77\)

b) \(log_{10}1;log_91\)

c) \(3^{log_315};7^{log_7\sqrt{2}}\)

d) \(log_88^{-10};log_55^{\sqrt{3}}\)

Bất phương trình logarit

$$1) \sqrt{log_{1/2}^{2} \frac{2x}{4-x} - 4} \leq \sqrt{5}$$
$$2)log_{2}(x-1)^{2} > 2log_{2} (x^{3} +x +1)$$
$$3)\frac{1}{log_{2}(4x)^{2} +3 } + \frac{1}{log_{4} 16x^{3}-2} <-1$$
$$4)log_{2} (4^{x}+4) < log_{\frac{1}{2}} (2^{x+1} -2)$$

\((\log_{2} (4x))^2-\log_{\sqrt{}2} (2x)=5\)

\(log_{\sqrt{3}}\left(\sqrt[5]{3}\right)=?\)

\(log_24.log_{\dfrac{1}{4}}2=?\)

m=? để \(log_{2\sqrt{2}+\sqrt{7}}\left(x-m+1\right)log_{2\sqrt{2}-\sqrt{7}}\left(mx-x^2\right)=0\)có nghiệm