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a)
\(x+\frac{11}{4}=\frac{17}{3}\)
\(x=\frac{17}{3}-\frac{11}{4}\)
\(x=\frac{35}{12}\)
b)
\(x-\frac{9}{5}=\frac{23}{7}\)
\(x=\frac{23}{7}+\frac{9}{5}\)
\(x=\frac{178}{35}\)
c)
\(x\)x \(\frac{7}{2}=\frac{19}{4}\)
\(x=\frac{19}{4}:\frac{7}{2}\)
\(x=\frac{19}{14}\)
d)
\(x:\frac{8}{3}=\frac{13}{3}\)
\(x=\frac{13}{3}\)x \(\frac{8}{3}\)
\(x=\frac{104}{9}\)
a, \(\frac{4x}{3}=\frac{14x}{3}+5\)
\(\frac{4x}{3}-\frac{14x}{3}=5\)
\(\frac{-10x}{3}=5\)
x=-1,5
b, 3x-5x=2-4
-2x=-2
x=1
c, \(\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{11}-\frac{1}{12}\right)\) .x=2
\(\left(\frac{1}{1}-\frac{1}{12}\right).x=2\)
\(\frac{11}{12}.x=2\)
x=\(\frac{24}{11}\)
d, \(x=\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{101.103}\right)\)
\(x=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{101}-\frac{1}{103}\right)\)
x=\(\frac{1}{2}\left(1-\frac{1}{103}\right)\)
x=\(\frac{1}{2}.\frac{102}{103}\)
x=\(\frac{51}{103}\)
\(\left(x+17\right)\times21-3=7\)
\(\left(x+17\right)\times21=7+3\)
\(\left(x+17\right)\times21=10\)
\(x+17=10:21\)
\(x+17=\frac{10}{21}\)
\(x=\frac{10}{21}-17\)
\(x=-\frac{347}{21}\)
\(b,5^{x-1}-13=612\)
\(5^{x-1}=612+13\)
\(5^{x-1}=625\)
\(5^{x-1}=5^4\)
\(x-1=4\)
\(x=4+1\)
\(x=5\)
\(e,3^x=3^2\times9\)
\(3^x=3^2\times3^2\)
\(3^x=3^4\)
\(\Rightarrow x=4\)
\(f,2^{3x+4}=1024\)
\(2^{3x+4}=2^{10}\)
\(\Rightarrow3x+4=10\)
\(\Rightarrow3x=10-4\)
\(\Rightarrow3x=6\)
\(\Rightarrow x=2\)
\(\frac{2}{5}x+\frac{3}{10}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.........+\frac{1}{9}-\frac{1}{10}\)
\(\frac{2}{5}x+\frac{3}{10}=1-\frac{1}{10}=\frac{9}{10}\)
\(\frac{2}{5}x=\frac{9}{10}-\frac{3}{10}=\frac{3}{5}\)
\(x=\frac{\frac{3}{5}}{\frac{2}{5}}=\frac{3}{2}\)
Ta có: \(\frac{1}{1x2}\)+ \(\frac{1}{2x3}\)+ \(\frac{1}{3x4}\)+ \(\frac{1}{4x5}\)+ .....+ \(\frac{1}{9x10}\)
= \(1-\left(\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-.....-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)
= 1 - \(\frac{1}{10}\)
= \(\frac{9}{10}\)
3^x = 3^3.3^5
3^x = 3^ (5 +3)
3^x = 3^5
=> x = 5
2, 2^x = 4 .128
2^x = 2^2 . 2^7
2^x = 2^ ( 2 +7)
2^x = 2^9
=> x = 9
3, 2^x.3^x = 2^2 . 3^2
=> x = 2