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Bài 1:
2\(x\) = 4
2\(^x\) = 22
\(x=2\)
Vậy \(x=2\)
Bài 2:
2\(^x\) = 8
2\(^x\) = 23
\(x=3\)
Vậy \(x=3\)
a) 5x+x+1=\(\dfrac{125}{25}\)
\(\leftrightarrow\) 52x+1 =51
\(\leftrightarrow\) 2x+1=1
\(\leftrightarrow\)2x=0
\(\leftrightarrow\) x=0
Bài 9,
62x73+36x33=36x73+36x27=36(73+27)=36x100=3600.
197-\([\)6x(5-1)2+20220\(]\):5=197-\([\)6x16+1\(]\):5=197-97:5=197-97/5=888/5.
Bài 10,
21-4x=13
=>4x=21-13=8
=>x=8:4=2.
30:(x-3)+1=45:43=42=16
=>30:(x-3)=16-1=15
=>x-3=30:15=2
=>x=2+3=5.
(x-1)3+5x6=38
=>(x-1)3+30=38
=>(x-1)3=38-30=8=23
=>x-1=2
=>x=3.
a) \(5\left(x+7\right)-10=2^3\cdot5\)
\(\Rightarrow5\left(x+7\right)-10=40\)
\(\Rightarrow5\left(x+7\right)=40+10\)
\(\Rightarrow x+7=\dfrac{50}{5}\)
\(\Rightarrow x+7=10\)
\(\Rightarrow x=10-7\)
\(\Rightarrow x=3\)
b) \(9x-2\cdot3^2=3^4\)
\(\Rightarrow9x-18=81\)
\(\Rightarrow9x=81+18\)
\(\Rightarrow9x=99\)
\(\Rightarrow x=\dfrac{99}{9}\)
\(\Rightarrow x=11\)
c) \(5^{25}\cdot5^{x-1}=5^{25}\)
\(\Rightarrow5^{x-1}=5^{25}:5^{25}\)
\(\Rightarrow5^{x-1}=1\)
\(\Rightarrow5^{x-1}=5^0\)
\(\Rightarrow x-1=0\)
\(\Rightarrow x=1\)
a) 25+x=0
x=0-25
x=-25
b)\(2^x:2^{19}=2^{25}\)
\(2^x=2^{25}.2^{19}\)
\(2^x=2^{44}\)
=>x=44
c)\(5^x.5^{18}=5^{54}\)
\(5^x=5^{54}:5^{18}\)
\(5^x=5^{36}\)
=>x=36
1.
a) \(3^2\cdot2^5-\left(3\cdot6^2-x\right)=120\\ 9\cdot32-\left(3\cdot36-x\right)=120\\ 288-\left(108-x\right)=120\\ 288-108+x=120\\ 180+x=120\\ \Rightarrow x=-60\)
Vậy x = -60
b) \(\left(x+3\right)\cdot2^3-2^2\cdot5=2^2\cdot3^5\\ \left(x+3\right)\cdot8-4\cdot5=4\cdot243\\ \left(x+3\right)\cdot8-20=972\\ \Rightarrow8\left(x+3\right)=992\\ \Rightarrow x+3=124\\ \Rightarrow x=121\)
Vậy x = 121
2.
a) \(5^{x-1}-13=612\\ \Rightarrow5^{x-1}=625=5^3\\ \Rightarrow x-1=3\\ \Rightarrow x=4\)
Vậy x = 4
b) \(5^x\cdot5^3=125\\ 5^{x+3}=5^3\\ \Rightarrow x+3=3\\ \Rightarrow x=0\)
Vậy x = 0
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Ta có:
\(5^x+5^{x+2}=210\)
\(\Leftrightarrow5^x\left(1+5^2\right)=210\)
\(\Leftrightarrow5^x\cdot26=210\)
\(5^x=\frac{105}{13}\)