Tìm số tự nhiên n biết :
a.3n= 27
b. 5n= 625
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`@` `\text {Ans}`
`\downarrow`
`1+2+3+4+5+6+7+8`
`= (1 +5) + (2+8) + (3+7) + (4+6)`
`= 6 + 10 + 10 + 10`
`= 36`
\(198+789+502+34\)
\(=\left(198+502\right)+\left(789+34\right)\)
\(=700+823\)
\(=1523\)
\(198+789+502+34\)
\(=\left(198+502\right)+\left(766+34\right)-23\)
\(=700+800-23\)
\(=1500-23\)
\(=1477\)
\(158+445+342+555\)
\(=\left(158+342\right)+\left(445+555\right)\)
\(=500+1000\)
\(=1500\)
\(158+445+342+555\)
\(=\left(158+342\right)+\left(445+555\right)\)
\(=500+1000\)
\(=1500\)
\(10+2x=45\div4^5\)
\(10+2x=45\div1024\)
\(10+2x=\dfrac{45}{1024}\)
\(2x=\dfrac{45}{1024}-10\)
\(2x=-\dfrac{10195}{1024}\)
\(x=-\dfrac{10195}{1024}:2=-\dfrac{10195}{2048}\)
\(714+382+286+318\)
\(=\left(714+286\right)+\left(382+318\right)\)
\(=1000+700\)
\(=1700\)
\(15\cdot6\cdot4\cdot125\cdot8\)
\(=\left(15\cdot4\right)\cdot6\cdot\left(125\cdot8\right)\)
\(=60\cdot6\cdot1000\)
\(=60000\cdot6\)
\(=360000\)
15.6.4.125.8
= 3.5.2.3.4.(125.8)
= (5.2).3.3.4.1000
=10.36.1000
=360000
14.25.6.7
= 7.2.25.3.2.7
=(25.2.2).3.7.7
=100.3.7.7
=300.7.7
=2100.7
=14700
`@` `\text {Ans}`
`\downarrow`
`24*3*5*10`
`= 2^3*3*3*5*5*2`
`= 2^4*3^2*5^2`
`= 4^2*3^2*5^2`
`= (4*3*5)^2`
`= 60^2`
`= 3600`
\(24\cdot3\cdot5\cdot10\)
\(=3\cdot3\cdot2\cdot3\cdot5\cdot10\)
\(=\left(3\cdot3\cdot3\right)\cdot\left(2\cdot5\right)\cdot10\)
\(=27\cdot10\cdot10\)
\(=27\cdot100\)
\(=2700\)
2+4+6+8+...+(2x)=120
=> (1+2+3+4+...+x).2=120
=> 1+2+3+4+...+x = 120:2=60
=> (x+1).x : 2 = 60
=> (x+1).x=60.2 = 120
=> Không có x thỏa mãn
`@` `\text {Ans}`
`\downarrow`
`a.`
`3^n = 27` phải k c?
`3^n = 27`
`=> 3^n = 3^3`
`=> n=3`
Vậy, `n=3`
TH2 (đề):
`3n = 27`
`=> n = 27 \div 3`
`=> n=9`
Vậy, `n=9`
`b.`
TH1:
`5^n = 625`
`=> 5^n = 5^4`
`=> n = 4`
Vậy, `n=4`
TH2:
`5n = 625`
`=> n = 625 \div 5`
`=> n = 125`
Vậy, `n=125`