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Bài làm:
Ta có: \(3^x+5.3^{x+2}=414\)
\(\Leftrightarrow3^x\left(1+5.3^2\right)=414\)
\(\Leftrightarrow3^x.46=414\)
\(\Leftrightarrow3^x=9=3^2\)
\(\Rightarrow x=2\)
3x + 5 . 3x + 2 = 414
<=> 3x + 5 . 3x . 32 = 414
<=> 3x ( 1 + 45 ) = 414
<=> 3x . 46 = 414
<=> 3x = 9
<=> 3x = 32
<=> x = 2
<=> 3x+5.32.3x=414
<=> 3x+45.3x=414
<=> 46.3x=414
=> 3x=414:46
=> 3x=9=32
=> x=2
c, \(5^{x+4}-3\cdot5^{x+3}=2\cdot5^{11}\)
\(\Leftrightarrow5^{x+3}\cdot5-3\cdot5^{x+3}=2\cdot5^{11}\)
\(\Leftrightarrow5^{x+3}\left(5-3\right)=2\cdot5^{11}\)
\(\Leftrightarrow5^{x+3}\cdot2=2\cdot5^{11}\)
\(\Leftrightarrow5^{x+3}=5^{11}\)
\(\Leftrightarrow x+3=11\)
\(\Leftrightarrow x=8\)
Vậy x = 8
d, \(2^x+2^{x+1}+2^{x+2}+2^{x+3}+2^{x+4}+2^{x+5}=480\)
\(\Leftrightarrow2^x\left(1+2+2^2+2^3+2^4+2^5\right)=480\)
\(\Leftrightarrow2^x\cdot63=480\)
\(\Leftrightarrow2^x=\frac{160}{21}\)
\(\Leftrightarrow x\approx2,93\)
5.3x = 5.34
=> x = 4
5.34 = 7.35 - 2.35
= 35 . (7 - 2)
= 5. 35
=> 3x = 35
=> x = 5
\(a,12,3\cdot4,7+5,3\cdot12,3-1,4\cdot7,5+7,5\cdot5,4\)
\(=12,3\cdot\left(4,7+5,3\right)-7,5\cdot\left(1,4+5,4\right)\)
\(=12,3\cdot10-7,5\cdot6,8\)
\(=123-51\)
\(=72.\)
\(b,3\cdot x-1=\frac{3}{4}:\frac{15}{16}\)
\(\Leftrightarrow3\cdot x-1=\frac{3}{4}\cdot\frac{16}{15}\)
\(\Leftrightarrow3\cdot x-1=\frac{4}{5}\)
\(\Leftrightarrow3\cdot x=\frac{4}{5}+1\)
\(\Leftrightarrow3\cdot x=\frac{9}{5}\)
\(\Leftrightarrow x=\frac{9}{5}\div3\)
\(\Leftrightarrow x=\frac{9}{5}\cdot\frac{1}{3}\)
\(\Leftrightarrow x=\frac{3}{5}\)
a) \(12,3\times4,7+5,3\times12,3-1,4\times7,5+7,5\times5,4\)
\(=12,3\times\left(4,7+5,3\right)+7,5\times\left(5,4-1,4\right)\)
\(=12,3\times10+7,5\times4\)
\(=123+30\)
\(=153\)
b) \(3.x-1=\frac{3}{4}:\frac{15}{16}\)
\(\Rightarrow3.x-1=\frac{4}{5}\)
\(\Rightarrow3.x=\frac{9}{5}\Rightarrow x=\frac{3}{5}\)
a,8.6+288:(x-3)^2=50
48+288:(x-3)^2=50
288:(x-3)^2=2
(x-3^2=288:2
(x-3)^2=144=12^2
x=12+3
=>x=15
x=100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
3^x+5.3^x+2
3^x + 5. 3^x + 2 = 0
3^x (1 +5) + 2 =0
3^x. 6 + 2 = 0
3^x. 6 = 0-2
3^x .6 = - 2
3^x = -2 : 6
3^x = -1/2
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