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a) 232 - (3x + 2).5 = 23.52
232 - (3x + 2).5 = 8.25
232 - 5.(3x + 2) = 200
-5.(3x + 2) = 200 - 232
-5.(3x + 2) = -32
3x + 2 = (-32) : (-5)
3x + 2 = 32/5
3x = 32/5 - 2
3x = 22/5
x = 22/5 : 3
x = 22/15
\(a)232-\left(3x+2\right).5=2^3.5^2\)
\(\Leftrightarrow232-\left(3x+2\right).5=200\)
\(\Leftrightarrow\left(3x+2\right).5=32\)
\(\Leftrightarrow3x+2=6.4\)
\(\Leftrightarrow3x=4.4\)
\(\Leftrightarrow\frac{22}{15}\)
\(b)3.5^x-10^0=74\)
\(\Leftrightarrow3.5^x=75\)
\(\Leftrightarrow5^x=25\)
\(\Leftrightarrow5^x=5^2\)
\(\Leftrightarrow x=2\)
\(c)4^{2x+4}=64\)
\(\Leftrightarrow4^{2x+4}=4^3\)
\(\Leftrightarrow2x+4=3\)
\(\Leftrightarrow x=-\frac{1}{2}\)
\(d)5^{x-1}+5^x=100\)
\(\Leftrightarrow5^x.\frac{1}{5}+5^x=100\)
\(\Leftrightarrow5^x\left(\frac{1}{5}+1\right)=100\)
\(\Leftrightarrow5^x=\frac{250}{3}\)
Chưa nghĩ ra. Các câu khác tương tự như các câu trên.
\(\Rightarrow5^{3x+2}< 10^{18}\div2^{18}\)
\(\Rightarrow5^{3x+2}< 5^{18}\)
\(3x+2< 18\)
\(x< \frac{16}{3}\)
\(2^3\cdot5-\left(x+3^2\right)=10\)
\(\left(x+9\right)=2^3\cdot5-10\)
\(\left(x+9\right)=30\)
\(x=21\)
Vậy,......
\(2^3.5-\left(x+3^2\right)=10\)
\(\Rightarrow\) \(40-\left(x+3^2\right)=10\)
\(\Rightarrow\) \(x+3^2=30\)
\(\Rightarrow\) \(x+9=30\)
\(\Rightarrow\) \(x=30-9\)
\(\Rightarrow\) \(x=21\)
a: \(S=\dfrac{-1}{2}\cdot\dfrac{-2}{3}\cdot...\cdot\dfrac{-99}{100}=-\dfrac{1}{100}\)
c: \(5S_3=5^6+5^7+...+5^{101}\)
\(\Leftrightarrow4\cdot S_3=5^{101}-5^5\)
hay \(S_3=\dfrac{5^{101}-5^5}{4}\)
d: \(S_4=7\cdot\left(\dfrac{1}{10}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}+...+\dfrac{1}{69}-\dfrac{1}{70}\right)\)
\(=7\left(\dfrac{1}{10}-\dfrac{1}{70}\right)=7\cdot\dfrac{6}{70}=\dfrac{6}{10}=\dfrac{3}{5}\)
\(3^{x+1}.5-10:2+5=15\)
`3^(x+1) . 5 - 5 + 5 = 15`
`3^(x+1) .5 - 5=15-5`
`3^(x+1).5 -5 = 10`
`3^(x+1).5=10+5`
`3^(x+1).5=10=5`
`3^(x+1) = 15 : 5`
`3^(x+1)=3`
`3^(x+1)=3^1`
`x+1=1`
`x=1-1`
`x=0`
Vậy `x=0`