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52\(x+1\) + 31 = 128
5\(2x+1\) + 3 = 128
5\(^{2x+1}\) = 128 - 3
5\(^{2x+1}\) = 125
5\(^{2x+1}\) = 53
2\(x\) + 1 = 3
2\(x\) = 3 - 1
2\(x\) = 2
\(x\) = 2: 2
\(x\) = 1
50+51+52+53+...+52010+52011
= 1+5+52+53+...+52010+52011
=(1+5)+(52+53)+...+(52010+52011)
= (1+5)+52(1+5)+...+52010(1+5)
= (1+5)(1+52+...+52010)
= 6.(1+52+...+52010) chia hết cho 6
=> đpcm
a, \(\frac{6^5\cdot27^2}{7^3\cdot9^5}=\frac{2^5\cdot3^5\cdot\left(3^3\right)^2}{7^3\cdot\left(3^2\right)^5}=\frac{2^5\cdot3^5\cdot3^6}{7^3\cdot3^{10}}=\frac{2^5\cdot3^{11}}{7^3\cdot3^{10}}=\frac{2^5\cdot3}{7^3}\)
b, \(\frac{12^7\cdot9^3}{8^5\cdot27^3}=\frac{3^7\cdot2^{12}\cdot3^6}{2^{15}\cdot3^9}=\frac{2^{12}\cdot3^{13}}{2^{15}\cdot3^9}=\frac{3^4}{2^3}\)
c, \(\frac{20^6\cdot8^2}{16^3\cdot25^3}=\frac{2^{12}\cdot5^6\cdot2^6}{2^{12}\cdot5^6}=2^6\)
a) 305 - 5x = 290
5.(61-x) = 290
61-x = 58
x = 3
b) (3x - 24) .25 = 26
3x - 24 = 2
3x = 18
x=6
c) 8 + 3.(x-5)2 = 35
3.(x-5)2 = 27
(x-5)2 = 9 = 32 = (-3)2
=> x - 5 = 3 => x = 8
x-5 = - 3 => x = 2
KL:>.
d) 21 chia hết cho x - 2
\(\Rightarrow x-2\inƯ_{\left(21\right)}=\left\{\pm1;\pm3;\pm7;\pm21\right\}.\)
..
rùi bn tự lập bảng xét giá trị nhé
a) \(7^5.7^6=7^{5+6}=7^{11}\)
b) \(5^{20}.5=5^{20+1}=5^{21}\)
c) \(7^9:7=7^{9-1}=7^8\)
d) \(25^3.5^2=\left(5^2\right)^3.5^2=5^{2.3}.5^2=5^6.5^2=5^{6+2}=5^8\)
\(\left(5^{65}:5^{60}\right):\left(5^1.5^3\right)=\left(5^{65-60}\right):\left(5^{1+3}\right)=5^5:5^4=5^{5-4}=5^1=5\)
=> \(5^5\): \(5^4\)= \(5^{5-4}=5^1=5\)