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Bài 2:
a: =>5x-1=0 hoặc 2x-1/3=0
=>x=1/6 hoặc x=1/5
b: =>x-1=4
=>x=5
c: \(\Leftrightarrow3^4< \dfrac{1}{3^2}\cdot3^{3x}< 3^{10}\)
=>4<3x-2<10
=>\(3x-2\in\left\{5;6;7;8;9\right\}\)
hay \(x=3\)
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\(\frac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\)
\(=\frac{5.\left(2^2\right)^{15}.\left(3^2\right)^9-2^2.3^{20}.\left(2^3\right)^9}{5.2^9.\left(2.3\right)^{19}-7.2^{29}.\left(3^3\right)^6}\)
\(=\frac{5.2^{30}.3^{18}-2^{29}.3^{20}}{5.2^{28}.3^{19}-7.2^{29}.3^{18}}\)
\(=\frac{2^{29}.3^{18}.\left(5.2-3^2\right)}{2^{28}.3^{18}.\left(5.3-7.2\right)}\)
\(=\frac{2.\left(5.2-3^2\right)}{5.3-7.2}=\frac{2.\left(5.2-3^2\right)}{15-14}=2.\left(5.2-3^2\right)\)
5.415.99−4.320.895.29.619−7.229.276
=5.(22)15.(32)9−22.320.(23)95.29.(2.3)19−7.229.(33)6
=5.230.318−229.3205.228.319−7.229.318
=229.318.(5.2−32)228.318.(5.3−7.2)
=2.(5.2−32)5.3−7.2 =2.(5.2−32)15−14 =2.(5.2−32)
\(\frac{6^{15}.9^{10}}{3^{34}.2^{13}}\)
\(=\frac{\left(2.3\right)^{15}.3^{20}}{3^{34}.2^{13}}\)
\(=\frac{2^{15}.3^{25}}{3^{34}.2^{13}}\)
\(=\frac{2^2.3}{1.1}=2^2.3=12\)
\(\frac{6^{15}.9^{10}}{3^{34}.2^{13}}=\frac{2^{15}.3^{15}.3^{20}}{3^{34}.2^{13}}=\frac{2^{15}.3^{35}}{3^{34}.2^{13}}=2^2.3=12\)