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\(8A=\frac{8^{19}+8}{8^{19}+1}=1+\frac{7}{8^{19}+1}\)
\(8B=\frac{8^{24}+8}{8^{24}+1}=1+\frac{7}{8^{24}+1}\)
\(\text{Vì }\frac{7}{8^{19}+1}>\frac{7}{8^{24}+1}\)
\(\Rightarrow8A>8B\)
\(\Rightarrow A>B\)
\(\text{Câu B làm tương tự nhé}\)
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a: \(\Leftrightarrow4^x\left(\dfrac{3}{2}+\dfrac{5}{3}\cdot4^2\right)=4^8\left(\dfrac{3}{2}+\dfrac{5}{3}\cdot4^2\right)\)
=>4^x=4^8
=>x=8
b: \(\Leftrightarrow2^x\cdot\dfrac{1}{2}+2^x\cdot2=2^{10}\left(2^2+1\right)\)
=>2^x=2^11
=>x=11
c: =>1/6*6^x+6^x*36=6^15(1+6^3)
=>6^x=6*6^15
=>x=16
d: \(\Leftrightarrow8^x\left(\dfrac{5}{3}\cdot8^2-\dfrac{3}{5}\right)=8^9\left(\dfrac{5}{3}\cdot8^2-\dfrac{3}{5}\right)\)
=>x=9
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\(\dfrac{2^{12}.3^5-2^{12}.3^6}{2^{12}.9^3+8^4.3^5}=\dfrac{2^{12}.\left(3^5-3^6\right)}{2^{12}.\left(3^2\right)^3+\left(2^3\right)^4.3^5}\\ =\dfrac{2^{12}.\left(3^5-3^6\right)}{2^{12}.\left(3^6+3^5\right)}=\dfrac{3^5-3^6}{3^6+3^5}\\ =\dfrac{3^5\left(1-3\right)}{3^5\left(1+3\right)}=\dfrac{-2.3^5}{4.3^5}=\dfrac{-2}{4}=-\dfrac{1}{2}\)
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Ta có: B = \(\frac{3^{15}.5^5+3^{12}.5^7}{3^{17}.5^6-3^{14}.5^8}\)
\(\Rightarrow\) B = \(\frac{3^3.3^{12}.5^5+3^{12}.5^2.5^5}{3^3.3^{14}.5^6-3^{14}.5^2.5^6}\)
\(\Rightarrow\) B = \(\frac{3^{12}.\left(3^3.5^5+5^2.5^5\right)}{3^{14}.\left(3^3.5^6-5^2.5^6\right)}\)
\(\Rightarrow\) B = \(\frac{3^{12}.\left[5^5.\left(3^3+5^2\right)\right]}{3^{14}.\left[5^6.\left(3^3-5^2\right)\right]}\)
\(\Rightarrow\) B = \(\frac{3^{12}.5^2.52}{3^{14}.5^6.2}\)
\(\Rightarrow\) B = \(\frac{1.1.26}{3^2.5.1}\) ( rút gọn nha bạn )
\(\Rightarrow\) B = \(\frac{26}{45}\). OK nhanhưng khi thi violympic thì bạn nên bấm máy tính cho nhanh để dành thời gian làm câu khó hơn nha.
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