24 . 54 =
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\(1+5^2+5^4+...+5^{2x}\left(1\right)=\dfrac{25^6-1}{24}\)
Đặt \(\left(1\right)=A\)
\(\Rightarrow A=1+5^2+...+5^{2x}\)
\(\Rightarrow5^2A=5^2+5^4+...+5^{2x+2}\)
\(\Rightarrow25A=5^2+5^4+...+5^{2x+2}\)
\(\Rightarrow25A-A=5^2+5^4+...+5^{2x+2}-1-5^2-...-5^{2x}\)
\(\Rightarrow24A=5^{2x+2}-1\)
\(\Rightarrow A=\dfrac{5^{2x+2}-1}{24}\)
Mà: \(A=\dfrac{25^6-1}{24}\)
\(\Rightarrow\dfrac{5^{2x+2}-1}{24}=\dfrac{\left(5^2\right)^6-1}{24}\)
\(\Rightarrow5^{2x+2}-1=5^{12}-1\)
\(\Rightarrow5^{2x+2}=5^{12}\)
\(\Rightarrow2x+2=12\)
\(\Rightarrow2x=10\)
\(\Rightarrow x=\dfrac{10}{2}\)
\(\Rightarrow x=5\)
\(24^{54}.54^{24}.2^{10}\\ =8^{54}.3^{54}.27^{54}.2^{54}.2^{10}\)
\(=2^{162}.3^{54}.3^{72}.2^{54}.2^{10}\\
=2^{226}.3^{126}\\
=2^{3.63+37}.3^{2.63}\\
=8^{63}.9^{63}.2^{37}\\
=72^{63}.2^{37}\)
Dễ thấy \(72^{63}.2^{37}⋮̸72^{63}\)
\(\dfrac{9}{54}=\dfrac{1}{6}=\dfrac{4}{24}< \dfrac{7}{24}\)
\(\dfrac{7}{24}< \dfrac{12}{24}< \dfrac{16}{24}=\dfrac{2}{3}\)
\(\dfrac{2}{3}< \dfrac{2+1}{3+1}=\dfrac{3}{4}\)
\(\dfrac{3}{4}< \dfrac{3+2}{4+2}=\dfrac{5}{6}\)
\(\dfrac{5}{6}< \dfrac{5+2}{6+2}=\dfrac{7}{8}\)
\(\dfrac{7}{8}< \dfrac{7+9}{8+9}=\dfrac{16}{17}\)
Vậy \(\dfrac{9}{54}< \dfrac{7}{24}< \dfrac{2}{3}< \dfrac{3}{4}< \dfrac{5}{6}< \dfrac{7}{8}< \dfrac{16}{17}\)
Sau 5 năm Hà ít hơn bố 24 tuổi
-Tk cho mk nha-
-Mk cảm ơn-
B3:
a. =-1250000
b. =-20000
c. =0
d. =-24000
B4:
a. =-4100
b. =-2700
c. =400
d. =1007
\(12,45\times x-0,45\times x+x=3,9.\)
\(\Leftrightarrow x\times\left(12,45-0,45+1\right)=3,9.\)
\(\Leftrightarrow x\times13=3,9.\)
\(\Leftrightarrow x=0,3.\)
Vậy \(x=0,3.\)
24.54=10000