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35 · 34 + 35 · 86 + 65 · 75 + 65 · 45
= 35 34 + 86 + 65 75 + 45
= 35 · 120 + 65 · 120
= 120 35 + 65
= 120 · 100
= 12000
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a: \(\Leftrightarrow4^x\left(\dfrac{3}{2}+\dfrac{5}{3}\cdot4^2\right)=4^8\left(\dfrac{3}{2}+\dfrac{5}{3}\cdot4^2\right)\)
=>4^x=4^8
=>x=8
b: \(\Leftrightarrow2^x\cdot\dfrac{1}{2}+2^x\cdot2=2^{10}\left(2^2+1\right)\)
=>2^x=2^11
=>x=11
c: =>1/6*6^x+6^x*36=6^15(1+6^3)
=>6^x=6*6^15
=>x=16
d: \(\Leftrightarrow8^x\left(\dfrac{5}{3}\cdot8^2-\dfrac{3}{5}\right)=8^9\left(\dfrac{5}{3}\cdot8^2-\dfrac{3}{5}\right)\)
=>x=9
a, \(\dfrac{4^2.4^3}{2^{10}}=\dfrac{4^5}{2^{10}}=\dfrac{\left(2^2\right)^5}{2^{10}}=\dfrac{2^{10}}{2^{10}}=1\)
b, \(\dfrac{2^7.9^3}{6^5.8^2}=\dfrac{2^7.\left(3^2\right)^3}{2^5.3^5.\left(2^3\right)^2}=\dfrac{2^7.3^6}{2^5.3^5.2^6}=\dfrac{3}{2^4}=\dfrac{3}{16}\)
c, \(\dfrac{9^7.5^6.125^9}{15^{15}.5^{18}}=\dfrac{3^{21}.5^6.5^{27}}{5^{15}.3^{15}.5^{18}}=\dfrac{3^{21}.5^{33}}{3^{15}.5^{33}}=3^6=729\)
d, \(\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\dfrac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\dfrac{2^{12}.3^9.\left(1+3.5\right)}{2^{11}.3^{11}.\left(2.3-1\right)}=\dfrac{2.16}{3^2.5}=\dfrac{32}{45}\)
Chúc bạn học tốt!!!
1)2x=211 =>x=11
2)4x=22x=(23)4=212
2x=12 =>x=6
3)(1/4)x=(1/8)6
(1/2)2x=(1/2)18
2x=18 =>x=9
1) 2x = 25 . 26
2x = 25+6
2x = 211
=> x = 11
2) 4x = 84
4x = 46
=> x =11
3) (\(\frac{1}{4}\))x = (\(\frac{1}{8}\))6
(\(\frac{1}{4}\))x = (\(\frac{1}{4}\))8
=> x = 8
\(a,\left[2^{17}+16^2\right]\cdot\left[9^{15}-3^{15}\right]\cdot\left[2^4-4^2\right]\)
\(=\left[2^{17}+16^2\right]\cdot\left[9^{15}-3^{15}\right]\cdot\left[16-16\right]\)
\(=\left[2^{17}+16^2\right]\left[9^{15}-3^{15}\right]\cdot0=0\)
\(b,\left[8^{2017}-8^{2015}\right]\cdot\left[8^{2014}\cdot8\right]\)
\(=8^{2015}\left[8^2-1\right]\cdot8^{2015}\)
\(=8^{2015}\cdot63\cdot8^{2015}=8^{4030}\cdot63\)sửa lại câu b , có vấn đề rồi
\(c,\frac{2^8+8^3}{2^5\cdot2^3}=\frac{2^8+\left[2^3\right]^3}{2^5\cdot2^3}=\frac{2^8+2^9}{2^8}=\frac{2^8\left[1+2\right]}{2^8}=3\)
2.a, \(2^6=\left[2^3\right]^2=8^2\)
Mà 8 = 8 nên 82 = 82 hay 26 = 82
b, \(5^3=5\cdot5\cdot5=125\)
\(3^5=3\cdot3\cdot3\cdot3\cdot3=243\)
Mà 125 < 243 nên 53 < 35
c, 26 = [23 ]2 = 82
Mà 8 > 6 nên 82 > 62 hay 26 > 62
d, 7200 = [72 ]100 = 49100
6300 = \(\left[6^3\right]^{100}\)= 216100
Mà 49 < 216 nên 49100 < 216100 hay 7200 < 6300
`@` `\text {Ans}`
`\downarrow`
\(5^{x-2}-3^2=2^4-\left(6^8\div6^6-6^2\right)\)
`\Rightarrow`\(5^x\div5^2-9=16-\left(6^2-6^2\right)\)
`\Rightarrow`\(5^x\div5^2-9=16\)
`\Rightarrow`\(5^x\div5^2=25\)
`\Rightarrow`\(5^x=5^2\cdot5^2\)
`\Rightarrow`\(5^x=5^4\Rightarrow x=4\)
Vậy, `x = 4.`
5ˣ⁻² - 3² = 2⁴ - (6⁸ : 6⁶ - 6²)
5ˣ⁻² - 9 = 16 - (36 - 36)
5ˣ⁻² - 9 = 16
5ˣ⁻² = 16 + 9
5ˣ⁻² = 25
5ˣ⁻² = 5²
x - 2 = 2
x = 2 + 2
x = 4