Biểu diễn các số sau đây theo a = ln2,b = ln5: ln500;ln1625;ln6,25;ln12+ln23+...+ln9899+ln99100.
1 câu trả lời
ln500=ln(2².5³)=2In 2+3In 5=2a+3b;
In $\frac{16}{25}$ =In ($2^{4}$.$5^{-2}$ )=4ln2–2ln5=4a–2b;
ln6,25=ln($5^{2}$ .$0,5^{2}$ )=2ln5+2ln0,5=2ln5–2ln2=2b–2a;
In $\frac{1}{2}$+In$\frac{2}{3}$+...+In$\frac{98}{99}$+In$\frac{99}{100}$
=ln1–ln2+ln2–ln3+…+ln99–ln100
=–ln100=–ln($2^{2}$.$5^{2}$=–2ln2–2ln5=–2a–2b
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