The value of log2 20 log2 80 ? log2 5 log2 320 is equal to

Question

The value of $\log_{2} 20 \log_{2} 80 - \log_{2} 5 \log_{2} 320$ is equal to

Smart Achievers · Accepted Answer

(4)

$\log_{2} 20 \log_{2} 80 - \log_{2} 5 \log_{2} 320$

$\log_{2} 20 \log_{2} 80 - \log_{2} 5 \log_{2} (20 \times 16)$

$= \log_{2} 20 \log_{2} (16 \times 5) - \log_{2} 5 \log_{2} (20 \times 16)$

$= \log_{2} 20 (\log_{2} 16 + \log_{2} 5) - \log_{2} 5 (\log_{2} 20 + \log_{2} 16)$

$= \log_{2} 20 \log_{2} 16 + \log_{2} 20 \log_{2} 5 - \log_{2} 5 \log_{2} 20 - \log_{2} 5 \log_{2} 16$

$= \log_{2} 16 (\log_{2} 20 - \log_{2} 5) + 0$

$= \log_{2} 16 \log_{2} \frac{20}{5} = \log_{2} 16 \log_{2} 4$

$= \log_{2} 2^{4} \log_{2} 2^{2} = 4 \times 2 = 8$ $(∵ \log_{2} 2 = 1)$

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