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520 : ( 515 . 6 + 515 . 19)
=5^20: [5^15(6+19)]
=5^20:5^15.5^2
=5^3
\(5^{20}\div\left(5^{15}.6+5^{15}.19\right)\)
\(=\)\(5^{20}\div\left[5^{15}.\left(6+19\right)\right]\)
\(=\)\(5^{20}\div\left[5^{15}.25\right]\)
\(=\)\(5^{20}\div\left[5^{15}.5^2\right]\)
\(=\)\(5^{20}\div5^{17}\)
\(=\)\(5^3\)
\(=\)\(125\)
S = 1 + 3 +32 + 33 + 34 + 35 + ... + 31000
=>3S=S = 3 +32 + 33 + 34 + 35 + ... + 31000+31001
=>3S-S=31001-1
=>S=(31001-1):2
\(S=1+3+3^2+3^3+3^4+....+3^{1000}\)
\(3S=3+3^2+3^3+3^4+3^5+....+3^{1001}\)
\(2S=3^{1001}-1\)
\(S=\frac{3^{1001}-1}{2}\)
\(16+\left(-6\right)+\left(-8\right)+7\)\(=16-6-8+7\)\(=\left(16-6\right)-\left(8-7\right)\)\(=10-1=9\)
\(\left(-8\right)-[\left(2015^0\right)-14+7]\)\(=-8-\left(1-14+7\right)\)\(=-8-\left(-6\right)=-2\)
\(\left(-31\right)-[82-\left(-17\right)]\)\(=-31-\left(82+17\right)\)\(=-31-99=-130\)
\(6\left(-2\right)^3+5\left(-4\right)-\left(-12\right)\)\(=6\left(-8\right)+\left(-20\right)+12\)\(=-48-20+12=-56\)
B=\(3^1+3^2+3^3+...+3^{300}\)
=\(\left(3^1+3^2\right)+\left(3^3+3^4\right)+...+\left(3^{299}+3^{300}\right)\)
=\(3\left(1+3\right)+3^3\left(1+3\right)+...+3^{299}\left(1+3\right)\)
=\(3.4+3^3.4+...+3^{299}.4\)
=\(\left(3+3^3+...+3^{299}\right).4\)
Vì 4\(⋮\)2 mà trong một tích có 1 ts chia hết cho 2 thì tích đó chia hết cho 2 \(\Rightarrow\)B\(⋮\)2
\(9.5^{x-3}=6.5^6+3.5^6\)
=> \(9.5^{x-3}=\left(6+3\right).5^6\)
=> \(9.5^{x-3}=9.5^6\)
=> \(5^{x-3}=5^6\)
=> x - 3 = 6
=> x = 9
23+3.x=5\(^6\)
23+3.x=15625
3.x=15625-23
3.x=15602
x=15602:3
x=5200,666667
Ta có:
23+3.x = \(5^6\)
\(\Leftrightarrow23+3.x=15625\)
\(\Leftrightarrow3.x=15625-23\)
\(\Leftrightarrow3.x=15602\)
<=> x = 15602:3
=> x =5200,666667
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