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1. Tính theo cách hợp lí:
\(2016.5^{2017}.\left(30.5^{2015}-5^{2016}\right)\)
\(=2016.5^{2017}.5^{2015}.\left(30-5\right)\)
\(=2016.5^{4032}.25\)
\(=2016.5^{4032}.5^2\)
\(=2016.5^{4034}\)
2. Tìm x:
\(4^{x+1}+4^0=65\)
\(\Leftrightarrow4^{x+1}+1=65\)
\(\Leftrightarrow4^{x+1}=65-1\)
\(\Leftrightarrow\left(2^2\right)^{x+1}=64\)
\(\Leftrightarrow2^{2x+2}=2^6\)
\(\Rightarrow2x+2=6\)
\(\Rightarrow2x=4\)
\(\Rightarrow x=2.\)
a)2n*23=64
C1:2n+3=26
=>n+3=6
n=6-3
n=3
C2:2n*8=64
2n=64/8
2n=8=23
=>n=3
2n*23=23*23
=>n=3
b)56:5n=625
C1:56-n=54
=>6-n=4
n=6-4
n=2
C2:5n=56/54
5n=52
=>n=2
C3:15625/5n=625
5n=15625/625
5n=52
=>n=2
\(a, 2^{x-1}+5.2^{x-2}=\frac{7}{32}\)
\(\Leftrightarrow2^x.2^{-1}+5.2^x.2^{-2}=\frac{7}{32}\)
\(\Leftrightarrow2^x.2^{-1}\left(1+5.2^{-1}\right)=\frac{7}{32}\)
\(\Leftrightarrow2^x.\frac{1}{2}.\frac{7}{2}=\frac{7}{32}\)
\(\Leftrightarrow2^x=\frac{1}{8}=2^{-3} \Rightarrow x=-3\)
\(b, 2^{5x-1}:8^x=32^5\)
\(\Leftrightarrow32^x.2^{-1}.8^{-x}=32^5\)
\(\Leftrightarrow2^{2x}.2^{-1}=32^5\)
\(\Leftrightarrow2^{2x-1}=2^{25}\)
\(\Leftrightarrow2x-1=25 \Rightarrow x=13\)
2.52x+3=52018-3.52017
2.52x+3=52017.5-3.52017
2.52x+3=52017(5-3)
2.52x+3=2.52017
=>52x+3=52017
=>2x+3=2017
2x=2017-3
2x=2014
x=2014/2
x=1007
Vậy x=1007
Vì |5-x| lớn hơn hoặc bằng 0
(y+2)^4 lớn hơn hoặc bằng 0
--> 5-x=0 và y+2=0
x=5 y=-2
\(x^5=243\)
\(\Rightarrow x^5=3^5\)
\(\Rightarrow x=3\)
\(x^5\)=243
\(x^5\)=\(3^5\)
\(\Rightarrow\)x=3