Question

Tìm x 

a/(1/3-5/6.x)³ + 21/54=5/6                                        b/1/12-1/13(1/2.x-1)⁴=1/16

c/(3/5)^x-1+5.(3/5)^x-1=54/25                                       d/ (2/3)^x+(2/3)^x+2=101/243

bài 2 So sánh 

a/1/27¹¹và  21/81⁸

b/1/399 và 1/11²¹

Answer 1

2) a) \(\frac{1}{27^{11}}=\frac{1}{\left(3^3\right)^{11}}=\frac{1}{3^{33}}\)

\(\frac{21}{81^8}=\frac{21}{\left(3^4\right)^8}=\frac{21}{3^{32}}=\frac{21.3}{3^{33}}=\frac{63}{3^{33}}>\frac{1}{3^{33}}\)

=> \(\frac{21}{81^8}>\frac{1}{27^{11}}\)

b) Rõ ràng : 399 < 11²¹ => \(\frac{1}{399}>\frac{1}{11^{21}}\)

Answer 2

a) \(\left(\frac{1}{3}-\frac{5}{6}x\right)^3=\frac{5}{6}-\frac{21}{54}\)=> \(\left(\frac{1}{3}-\frac{5}{6}x\right)^3=\frac{24}{54}=\frac{4}{9}\)

=> \(\frac{1}{3}-\frac{5}{6}x=\sqrt[3]{\frac{4}{9}}\) => \(\frac{5}{6}x=1-\sqrt[3]{\frac{4}{9}}\)

=> x = \(\frac{6}{5}-\frac{6}{5}.\sqrt[3]{\frac{4}{9}}\)

b) => \(\frac{1}{13}\left(\frac{1}{2}x-1\right)^4=\frac{1}{12}-\frac{1}{16}=\frac{1}{48}\)

=> \(\left(\frac{1}{2}x-1\right)^4=\frac{13}{48}\)

=>  \(\frac{1}{2}x-1=\sqrt[4]{\frac{13}{48}}\) hoặc \(\frac{1}{2}x-1=-\sqrt[4]{\frac{13}{48}}\)

=> \(x=2+2\sqrt[4]{\frac{13}{48}}\) hoặc \(x=2-2\sqrt[4]{\frac{13}{48}}\)