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a) \(\left(x-6\right)^3=\left(x-6\right)^2\Leftrightarrow\orbr{\begin{cases}x-6=1\Leftrightarrow x=7\\x-6=0\Leftrightarrow x=6\end{cases}}\)
b) \(\left(7.x-11\right)^3=2^5.5^2+200\)
\(\Leftrightarrow\left(7.x-11\right)^3=800+200\)
\(\Leftrightarrow\left(7.x-11\right)^3=1000\)
\(\Leftrightarrow\left(7.x-11\right)^3=10^3\)
\(\Leftrightarrow7x-11=10\Leftrightarrow7x=21\Leftrightarrow x=3\)
c) \(3+2^{x-1}=24-\left[4^2-\left(2^2-1\right)\right]\)
\(\Leftrightarrow3+2^{x-1}=24-\left[4^2-3\right]\)
\(\Leftrightarrow3+2^{x-1}=24-13\)
\(\Leftrightarrow3+2^{x-1}=11\)
\(\Leftrightarrow2^{x-1}=8\Leftrightarrow2^{x-1}=2^3\Leftrightarrow x-1=3\Leftrightarrow x=4\)
a)\(3^x.3=243\Leftrightarrow3^x=81\Leftrightarrow3^x=3^4\Leftrightarrow x=4\)
b) \(2^x.16^2=1024\Leftrightarrow2^x.256=1024\Leftrightarrow2^x=4\Leftrightarrow2^x=2^2\Leftrightarrow x=2\)
c) \(64:4^x=16^8\Leftrightarrow4^x=67108864\Leftrightarrow4^x=4^{13}\Leftrightarrow x=13\)
d) \(2^x=16\Leftrightarrow2^x=2^4\Leftrightarrow x=4\)
1)\(79-5\left(11-x\right)=34\)
\(\Rightarrow79-55+5x=34\)
\(\Rightarrow24+5x=34\)
\(\Rightarrow5x=-10\)
\(\Rightarrow x=-2\)
Vậy \(x=-2\)
2)\(32+2\left(7-x\right)=40\)
\(\Rightarrow32+14-2x=40\)
\(\Rightarrow46-2x=40\)
\(\Rightarrow2x=6\)
\(\Rightarrow x=3\)
Vậy \(x=3\)
3)\(\left(166-2x\right).8^9=2.8^{11}\)
\(\Rightarrow\left(83-x\right).2.8^9=2.8^{11}\)
\(\Rightarrow83-x=8^3\)
\(\Rightarrow83-x=512\)
\(\Rightarrow x=-429\)
Vậy \(x=-429\)
4)\(5^2.x-2^3.x=51\)
\(\Rightarrow x\left(5^2-2^3\right)=51\)
\(\Rightarrow x\left(25-8\right)=51\)
\(\Rightarrow17x=51\)
\(\Rightarrow x=3\)
Vậy \(x=3\)
5)\(3^x+4.3^x=5.3^7\)
\(\Rightarrow3^x\left(1+4\right)=5.3^7\)
\(\Rightarrow5.3^x=5.3^7\)
\(\Rightarrow3^x=3^7\)
\(\Rightarrow x=7\)
Vậy \(x=7\)
6)\(7.2^x-2^x=6.32\)
\(\Rightarrow2^x\left(7-1\right)=6.2^5\)
\(\Rightarrow6.2^x=6.2^5\)
\(\Rightarrow2^x=2^5\)
\(\Rightarrow x=5\)
Vậy \(x=5\)
7)\(15^{3-x}=225\)
\(\Rightarrow15^{3-x}=15^2\)
\(\Rightarrow3-x=2\)
\(\Rightarrow x=1\)
Vậy \(x=1\)
8)\(4.5^x-3=97\)
\(\Rightarrow4.5^x=100\)
\(\Rightarrow5^x=25\)
\(\Rightarrow5^x=5^2\)
\(\Rightarrow x=2\)
Vậy \(x=2\)
9)\(171-3.2^x=123\)
\(\Rightarrow3.2^x=48\)
\(\Rightarrow2^x=16\)
\(\Rightarrow2^x=2^4\)
\(\Rightarrow x=4\)
Vậy \(x=4\)
10)\(180-4.x^5=32\)
\(\Rightarrow4.x^5=148\)
\(\Rightarrow x^5=37\)//Đề có lỗi không ???
a) 52 . x = 62 + 82
\(5^2\cdot x=36+64\)
\(5^2\cdot x=100\)
\(x=100\div5^2\)
\(x=100\div25\)
\(x=4\)
b) ( 22 + 42 ) . x + 24 . 5 . x = 102
\(\left(4+16\right)\cdot x+16\cdot5\cdot x=100\)
\(x\cdot\left(20+80\right)=100\)
\(x\cdot100=100\)
\(x=100\div100\)
\(x=1\)
c ) 24 . x = 26
\(x=2^6\div2^4\)
\(x=2^{6-4}\)
\(x=2^2\)
\(x=4\)
d) 33 . x + 23 . x = 102
\(x\cdot\left(23+27\right)=100\)
\(x\cdot50=100\)
\(x=100\div50\)
\(x=2\)
e) 78 . x = 710
\(x=7^{10}\div7^8\)
\(x=7^{10-8}\)
\(x=7^2\)
\(x=49\)
\(a)x^{15}=x\)
\(\Rightarrow x^{15}-x=0\)
\(\Leftrightarrow x\left(x^{14}-1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x^{14}-1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=0\\x=1\end{cases}}}\)
Vậy....
\(b)2^x-15=17\)
\(\Leftrightarrow2^x=32\)
\(\Leftrightarrow2^x=2^5\)
\(\Rightarrow x=5\)
Vậy...
\(c)\left(2x+1\right)^3=125\)
\(\Leftrightarrow\left(2x+1\right)^3=5^3\)
\(\Rightarrow2x+1=5\)
\(\Leftrightarrow2x=4\Rightarrow x=2\)
Vậy...
_Y nguyệt_
\(a)x^{15}=x\)
\(\Rightarrow x=1\)
\(b)2^x-15=17\)
\(\Rightarrow2^x=32\)
\(\Rightarrow2^x=2^5\Rightarrow x=5\)
\(c)\left(2x+1\right)^3=125\)
\(\Rightarrow2x+1=5\)
\(\Rightarrow x=2\)
a)...
b)9^x-1=9
=>9^x-1=9^1
=>x-1=1
=>x=1+1
=>x=2
c)x^4=16
=>x^4=2^4
=>x=2
d)2^x:2^5=1
=>2^x=1.2^5
=>2^x=2^5
=>x=5
A
A