Question

Tìm x, biết:

\(\frac{1}{4}\cdot\frac{2}{6}\cdot\frac{3}{8}\cdot\frac{4}{10}\cdot\frac{5}{12}\cdot.....\cdot\frac{30}{62}\cdot\frac{31}{64}=2^x\)

Answer 1

\(\dfrac{1}{4}.\dfrac{2}{6}.\dfrac{3}{8}.\dfrac{4}{10}.\dfrac{5}{12}.....\dfrac{30}{62}.\dfrac{31}{64}=2^x\)

\(\Leftrightarrow\dfrac{1}{2.2}.\dfrac{2}{2.3}.\dfrac{3}{2.4}.\dfrac{4}{2.5}.\dfrac{5}{2.6}.....\dfrac{30}{2.31}.\dfrac{31}{2.32}=2^x\)

\(\Leftrightarrow\dfrac{1.2.3.4.5.....30.31}{2.2.2.3.2.4.2.5.2.6.....2.31.2.32}=2^x\)

\(\Leftrightarrow\dfrac{2.3.4.5.....30.31}{2^{31}.32.\left(2.3.4.5.....31\right)}=2^x\)

\(\Leftrightarrow\dfrac{1}{2^{31}.2^5}=2^x\)

\(\Leftrightarrow\dfrac{1}{2^{36}}=2^x\)

\(\Leftrightarrow2^{-36}=2^x\)

\(\Leftrightarrow x=-36\)

Answer 2

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Answer 3

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Và kết quả là đây

Answer 4

$\frac{1}{4}\cdot \frac{2}{6}\cdot \frac{3}{8}\cdot \frac{4}{10}\cdot \frac{5}{12}\cdot .....\cdot \frac{30}{62}\cdot \frac{31}{64}=2^x$

=>\(\frac{1}{2.2}\times\frac{2}{2.3}\times\frac{3}{2.4}\times\frac{4}{2.5}\times...\times\frac{30}{2.31}\times\frac{31}{2.32}=2^x\)

=>\(\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times...\times\frac{1}{2}\times\frac{1}{2.32}=2^x\)

=>\(\frac{1}{2^{31}.32}=2^x\)

=>\(\frac{1}{2^{31}.2^5}=2^x\)

=>\(\frac{1}{2^{36}}=2^x\)

=>\(2^{-36}=2^x\)

=>\(x=-36\)