1. a) 2012.24 + 77.2012 - 2012
= 2012. ( 24 + 77 - 1)
= 2012.100
= 201200.
b) 3^3.76 + 84.27 + 3^2.3.40
= 27. ( 76 + 84 + 40)
= 27. 200
= 5400.
c) 2^83 + 2^84 + 2^85 / 2^82 + 2^81 + 2^80
= 2^83.(1 + 2 + 2^2) / 2^80. (2^2 + 2 + 1)
= 2^83 / 2^80
= 2^3
= 8.
2. (Bài này mình biết làm câu a và câu d thôi, 2 câu kia mình ko hiểu lắm)
a) 5^2x+1=125
5^2x+1=5^3
=> 2x+1 = 3
2x = 3 - 1
2x = 2
x = 1.
d) (2x + 3)^4 = 81
(2x + 3)^4 = 3^4
=> 2x + 3 = 3
2x = 3 - 3
2x = 0
x = 0.
1, a, \(2012.24+77.2012-2012=2012\left(24+77-1\right)=2012.100=201200\)
b, \(3^3.76+84.27+3^2.3.40=3^3.76+84.3^3+3^3.40=3^3\left(76+84+40\right)=3^3.200=5400\)
c, \(\frac{2^{83}+2^{84}+2^{85}}{2^{82}+2^{81}+2^{80}}=\frac{2^{83}\left(1+2+2^2\right)}{2^{80}\left(2^2+2+1\right)}=\frac{2^{83}}{2^{80}}=2^3=8\)
2. a, \(5^{2x+1}=125\Rightarrow5^{2x+1}=5^3\Rightarrow2x+1=3\Rightarrow x=1\)
d, \(\left(2x+3\right)^4=81\Rightarrow\left(2x+3\right)^4=3^4\Rightarrow2x+3=3;-3\)
\(\Rightarrow\orbr{\begin{cases}2x+3=3\\2x+3=-3\end{cases}\Rightarrow\orbr{\begin{cases}x=0\\x=-3\end{cases}}}\)
1. a) 2012.24 + 77.2012 - 2012
= 2012. ( 24 + 77 - 1)
= 2012.100
= 201200.
b) 3^3.76 + 84.27 + 3^2.3.40
= 27. ( 76 + 84 + 40)
= 27. 200
= 5400.
c) 2^83 + 2^84 + 2^85 / 2^82 + 2^81 + 2^80
= 2^83.(1 + 2 + 2^2) / 2^80. (2^2 + 2 + 1)
= 2^83 / 2^80
= 2^3
= 8.
