Câu hỏi của Vũ Huy Hoàn

Question

a,$\text{(x-3)^3=27}$

b,$\left(2x+1\right)^3=125$

c, $2^x-15=17$

d,$\left(7x-11\right)^3=25.3^2+20$

e,$2^{x+3}+2^x=36$

f,$3^{x+4}+4+3^{x+2}=270$

i,$2.3^x=10.3^{12}+8.27^4$

k,\(\le...

Nguyễn Thanh Hằng · Accepted Answer

a) $\left(x-3\right)^3=27$

$\Rightarrow\left[{}\begin{matrix}\left(x-3\right)^3=3^3\\left(x-3\right)^3=\left(-3\right)^3\end{matrix}\right.$

$\Rightarrow\left[{}\begin{matrix}x-3=3\x-3=-3\end{matrix}\right.$

$\Rightarrow\left[{}\begin{matrix}x=6\x=0\end{matrix}\right.$ $\left(TM\right)$

Vậy $x\in\left\{0;6\right\}$ là giá trị cần tìm

b) $\left(2x+1\right)^3=125$

$\Rightarrow\left[{}\begin{matrix}\left(2x+1\right)^3=5^3\\left(2x+1\right)^3=\left(-5\right)^3\end{matrix}\right.$

$\Rightarrow\left[{}\begin{matrix}2x+1=5\2x+1=-5\end{matrix}\right.$

$\Rightarrow\left[{}\begin{matrix}x=3\x=-2\end{matrix}\right.$ $\left(TM\right)$

Vậy $x\in\left\{3;-2\right\}$ là giá trị cần tìm

c) $2^x-15=17$

$2^x=17+15$

$2^x=32$

$2^x=2^5$

$\Rightarrow x=5\left(TM\right)$

Vậy $x=5$ là giá trị cần tìmCâu trả lời: a) $\left(x-3\right)^3=27$

$\Rightarrow\left[{}\begin{matrix}\left(x-3\right)^3=3^3\\left(x-3\right)^3=\left(-3\right)^3\end{matrix}\right.$

$\Rightarrow\left[{}\begin{matrix}x-3=3\x-3=-3\end{matrix}\right.$

$\Rightarrow\left[{}\begin{matrix}x=6\x=0\end{matrix}\right.$ $\left(TM\right)$

Vậy $x\in\left\{0;6\right\}$ là giá trị cần tìm

b) $\left(2x+1\right)^3=125$

$\Rightarrow\left[{}\begin{matrix}\left(2x+1\right)^3=5^3\\left(2x+1\right)^3=\left(-5\right)^3\end{matrix}\right.$

$\Rightarrow\left[{}\begin{matrix}2x+1=5\2x+1=-5\end{matrix}\right.$

$\Rightarrow\left[{}\begin{matrix}x=3\x=-2\end{matrix}\right.$ $\left(TM\right)$

Vậy $x\in\left\{3;-2\right\}$ là giá trị cần tìm

c) $2^x-15=17$

$2^x=17+15$

$2^x=32$

$2^x=2^5$

$\Rightarrow x=5\left(TM\right)$

Vậy $x=5$ là giá trị cần tìm

Mashiro Shiina · Answer

$\left(x-3\right)^3=27$

$\Leftrightarrow\left(x-3\right)^3=3^3$

$\Leftrightarrow x-3=3\Rightarrow x=6$

$\left(2x+1\right)^3=125$

$\Leftrightarrow\left(2x+1\right)^3=5^3$

$\Leftrightarrow2x+1=5\Rightarrow2x=4\Rightarrow x=2$

$2^x-15=17$

$\Leftrightarrow2^x=15+17=32$

$\Leftrightarrow x=5$

$\left(7x-11\right)^3=25.3^2+20$

$\left(7x-11\right)^3=245$

$\left(7x-11\right)^3=\sqrt[3]{245}$

(lớp 6 chưa học cái này đề sai nhé)

$2^{x+3}+2^x=36$

$2^x.2^3+2^x=36$

$2^x\left(2^3+1\right)=36$

$2^x.9=36\Rightarrow2^x=4\Rightarrow x=2$

$3^{x+4}+4+3^{x+2}=270$

$3^{x+4}+3^{x+2}=270-4=266$

$3^x.3^4+3^x.3^2=266$
$3^x\left(3^4+3^2\right)=266$(đề cũng sai)

$2.3^x=10.3^{12}+8.27^4$

$2.3^x=5314410+4251528$

$2.3^x=9565938$

$3^x=9565938:2=4782969$

$\Leftrightarrow x=14$

$\left(2x-5\right)^5=3^{10}$

$\Leftrightarrow\left(2x-5\right)^5=\left(3^2\right)^5$

$\left(2x-5\right)^5=9^5$

$\Leftrightarrow2x-5=9\Rightarrow2x=14\Rightarrow x=7$Câu trả lời: $\left(x-3\right)^3=27$