\(\text{Tìm }x\text{ biết : }\)
\(3^x=3\cdot3^2\cdot3^3\cdot3^4\cdot3^5\cdot...\cdot3^{99}\cdot3^{100}\)
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Rút gọn biểu thức sau:
B = \(3\cdot3^2\cdot3^3\cdot3^4\cdot...\cdot3^{100}\).
\(3B=3^2.3^3.....3^{101}\)
\(3B-B=3^{101}-3\)
\(2B=3^{101}-3\)
\(B=\frac{3^{101}-3}{2}\)
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Tính
\(\frac{5\cdot\left(2^2\cdot3^2\right)^9\cdot\left(2^2\right)^6-2\cdot\left(2^2\cdot3\right)^{14}\cdot3^4}{5\cdot2^{28}\cdot3^{18}+7\cdot2^{29}\cdot3^{18}}\)
\(\frac{5.\left(2^2.3^2\right)^9.\left(2^2\right)^6-2.\left(2^2.3\right)^{14}.3^4}{5.2^{28}.3^{18}+7.2^{29}.3^{18}}\)
\(=\frac{5.2^{18}.3^{18}.2^{12}-2.2^{28}.3^{14}.3^4}{2^{28}.3^{18}.\left(5+7.2\right)}\)
\(=\frac{5.2^{30}.3^{18}-2^{29}.3^{18}}{2^{28}.3^{18}.19}=\frac{2^{28}.3^{18}.\left(5.4-2\right)}{2^{28}.3^{18}.19}\)
\(=\frac{5.4-2}{19}=\frac{18}{19}\)
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Rút gọn biểu thức sau:
B = \(3\cdot3^2\cdot3^3\cdot3^4\cdot...\cdot3^{100}\).
\(B=3+3^2+3^3+...+3^{100}\)
\(\Rightarrow3B=3^2+3^3+3^4+...+3^{101}\)
\(\Rightarrow3B-B=\left(3^2+3^3+3^4+...+3^{101}\right)-\left(3+3^2+3^3+...+3^{100}\right)\)
\(\Rightarrow2B=3^{101}-3\)
\(\Rightarrow B=\dfrac{3^{101}-3}{2}\)
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thực hiện phép tính
A=\(\frac{5\cdot\left(2^2\cdot3^2\right)^9\cdot\left(2^2\right)^6-2\cdot\left(2^2\cdot3\right)^{14}\cdot3^4}{5\cdot2^{28}\cdot3^{18}-7\cdot2^{29}\cdot3^{18}}\)
A =\(\frac{5\cdot\left(2^2\cdot3^2\right)^9\cdot\left(2^2\right)^6-2\cdot\left(2^2\cdot3\right)^{14}}{5\cdot2^{28}\cdot3^{18}-7\cdot2^{29}\cdot3^{18}}\cdot3^4\)
Hãy thực hiện phép tính
\(\frac{1}{2\cdot3}+\frac{1}{3\cdot\text{4}}+\frac{1}{4\cdot5}+....+\frac{1}{x\cdot\left(x+1\right)}=\frac{99}{100}\)
- Tìm x giải hộ giùm Luka nga~
\(\Leftrightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{99}{100}\)
\(\Leftrightarrow1-\frac{1}{x+1}=\frac{99}{100}\)
\(\frac{100}{100}-\frac{1}{x+1}=\frac{99}{100}\)
\(\frac{1}{x+1}=\frac{1}{100}\)
\(\Rightarrow x+1=100\)
\(x=99\)
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1:rút gọn
\(\dfrac{11\cdot3^{22}\cdot3^7-9^{15}}{\left(2\cdot3^{14}\right)^2}\)
2: tìm x
\(\dfrac{3\cdot\left(x-2\right)}{4}-\dfrac{2\cdot\left(1+2x\right)}{3}=1\dfrac{1}{4}-5\cdot\dfrac{\left(1+3x\right)}{6}-\dfrac{x-2}{12}\)
\(\dfrac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}\)
\(=\dfrac{11.3^{29}-\left(3^2\right)^{15}}{2^2.3^{28}}\)
\(=\dfrac{11.3^{29}-3^{30}}{2^2.3^{28}}\)
\(=\dfrac{3^{29}\left(11-3\right)}{2^2.3^{28}}\)
\(=\dfrac{3^{29}.2^3}{2^2.3^{28}}\)
\(=\dfrac{3.2}{1.1}=6\)
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\(P=\frac{1}{1\cdot2\cdot3\cdot\text{4}}+\frac{1}{2\cdot3\cdot4\cdot5}+.........+\frac{1}{102\cdot103\cdot104\cdot105}\)
tính
A = \(\frac{5\cdot\left(2^2\cdot3^2\right)^9\cdot\left(2^2\right)^6-\left(2^2\cdot3\right)^{14}9^4}{5\cdot2^{28}\cdot3^{18}-7\cdot2^{29}\cdot3^{18}}\)
ta có \(\frac{5\left(2^2.3^2\right)^9.\left(2^2\right)^6-\left(2^2.3\right)^{14}.9^{14}}{5.2^{28}.3^{18}-7.2^{29}.3^{18}}\)
\(=\frac{5.2^{18}.3^{18}.2^{12}-2^{28}.3^{14}.3^8}{2^{28}.3^{18}\left(5.1.1-7.2.1\right)}\)
\(=\frac{2^{28}.3^{18}\left(5.1.3.2^2-1.3^4\right)}{2^{28}.3^{18}\left(5-14\right)}\)
\(=\frac{60-81}{5-14}=\frac{7}{3}\)
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