Đáp án:
Bài 1:
a)
$3n+7\vdots n-1$
$\Rightarrow 3n+7-3(n-1)\ \vdots \ n-1$
$\Rightarrow 10\ \vdots\ n-1$
$\Rightarrow n-1\in Ư(10)=\pm1,\pm2,\pm5,\pm10$
Ta có bảng sau:
\begin{array}{|c|c|c|} \hline n-1&-10&-5&-2&-1&1&2&5&10\\ \hline n&-9(loại)&-4(loại)&-1(loại)&0(tm)&2(tm)&3(tm)&6(tm)&11(tm)\\ \hline \end{array}
Vậy $x\in \{0,2,3,6,11\}$
b)
$27-5n\vdots 2-n$
$\Rightarrow 27-5n-5(2-n)\ \vdots \ 2-n$
$\Rightarrow 17\ \vdots\ 2-n$
$\Rightarrow 2-n\in Ư(17)=\pm1,\pm17$
Ta có bảng sau:
\begin{array}{|c|c|c|} \hline 2-n&-17&-1&1&17\\ \hline n&19(tm)&3(tm)&1(tm)&-15(loại)\\ \hline \end{array}
Vậy $x\in\{19,3,1\}$
Bài 2:
a)
$16^x=128^4$
$(2^4)^x=(2^7)^4$
$2^{4x}=2^{28}$
$4x=28$
$x=7(tm)$
Vậy $x=7$
b)
$5^x.5^{x+1}.5^{x+2}=10^{18}:2^{18}$
$5^{x+x+1+x+2}=(5.2)^{18}:2^{18}$
$5^{3x+3}=5^{18}.2^{18}:2^{18}$
$5^{3x+3}=5^{18}$
$3x+3=18$
$3x=15$
$x=5(tm)$
Vậy $x=5$
