Tìm số nguyên x, biết:
a) | x + 2010 | = 2011
b) 2 < | x- 2011| < 5
. Tìm x
a) 2 $2^{x+5}$ = 128 3.$3^{x}$ = 81
b) 3.$3^{x}$=81
c) 25+$5^{x}$. $5^{x}$ = 650
d) $3^{x}$.$3^{x+1}$-81=162
Tìm số nguyên x, biết:
a) | x + 2010 | = 2011
b) 2 < | x- 2011| < 5
. Tìm x
a) 2 $2^{x+5}$ = 128 3.$3^{x}$ = 81
b) 3.$3^{x}$=81
c) 25+$5^{x}$. $5^{x}$ = 650
d) $3^{x}$.$3^{x+1}$-81=162
`1`
`a)|x+2010|=2011`
`→` \(\left[ \begin{array}{l}x+2010=2011\\x+2010=-2011\end{array} \right.\)
`→` \(\left[ \begin{array}{l}x=1\\x=-4021\end{array} \right.\)
Vậy `x∈{1;-4021}`
`b)2<|x-2011|<5`
`→x∈{3;4}`
`→` \(\left[ \begin{array}{l}|x-2011|=3\\|x-2011|=4\end{array} \right.\)
`→` \(\left[ \begin{array}{l}x-2011=3\\x-2011=-3\\x-2011=4\\x-2011=-4\end{array} \right.\)
`→` \(\left[ \begin{array}{l}x=2014\\x=2008\\x=2015\\x=2007\end{array} \right.\)
Vậy `x∈{2007;2008;2014;2015}`
`2`
`a)2.2^(x+5)=128`
`→2^(x+5)=64`
`→2^(x+5)=2^6`
`→x+5=6`
`→x=1`
Vậy `x=1`
`b)3.3^x=81`
`→3^x=27`
`→3^x=3^3`
`→x=3`
Vậy `x=3`
`c)25+5^x . 5^x=650`
`→5^(2x)=625`
`→5^(2x)=5^4`
`→2x=4`
`→x=2`
Vậy `x=2`
`d)3^x . 3^(x+1) – 81=162`
`→3^(2x+1)=243`
`→3^(2x+1)=3^5`
`→2x+1=5`
`→2x=4`
`→x=2`
Vậy `x=2`
Đáp án + Giải thích các bước giải:
Ta có :
`a)|x+2010|=2011`
`→` \(\left[ \begin{array}{l}x+2010=2011\\x+2010=-2011\end{array} \right.\)
`→` \(\left[ \begin{array}{l}x=1\\x=-4021\end{array} \right.\)
Vậy `x∈{1;-4021}`
`b)2<|x-2011|<5`
Mà `|x-2011|∈Z`
`->|x-2011|∈{3;4}`
`→x-2011∈{±3;±4}`
`→x∈{2014;2015;2008;2007}`
Vậy `x∈{2014;2015;2008;2007}`
`———-`
`a)2.2^{x+5}=128`
`→2^{x+6}=2^{7}`
`→x+6=7`
`→x=1`
`b)3.3^{x}=81`
`->3^{x+1}=3^{4}`
`→x+1=4`
`→x=3`
`c)25+5^{x}.5^{x}=650`
`->5^{2x}=650-25`
`->5^{2x}=625`
`->5^{2x}=5^{4}`
`->2x=4`
`->x=2`
`d)3^{x}.3^{x+1}-81=162`
`->3^{2x+1}=162+81`
`->3^{2x+1}=243`
`->3^{2x+1}=3^{5}`
`->2x+1=5`
`->2x=4`
`->x=2`