Solve the following mathematical problems with sufficient calculations.

Simplify: $\frac{\log \sqrt{27} + l o g 8 - l o g \sqrt{1000}}{\log 1.2}$

Created: 1 year ago | Updated: 1 year ago

Updated: 1 year ago

$\frac{\log \sqrt{27} + l o g 8 - l o g \sqrt{1000}}{\log 1.2}$

$= \frac{\log \sqrt{3^{3}} + \log 2^{3} - \log \sqrt{{(2 \times 5)}^{3}}}{\log \frac{12}{10}}$

$= \frac{\log 3^{\frac{3}{2}} + \log 2^{3} - \log \sqrt{2^{3} \times 5^{3}}}{\log \frac{6}{5}}$

$= \frac{\frac{3}{2} \log 3 + 3 \log 2 - \log (2^{\frac{3}{2}} \times 5^{\frac{3}{2}})}{\log 6 - \log 5}$

$= \frac{\frac{3}{2} \log 3 + 3 \log 2 - \log (2^{\frac{3}{2}} \times 5^{\frac{3}{2}})}{\log 6 (3 \times 2) - \log 5}$

$= \frac{\frac{3}{2} \log 3 + 3 \log 2 - \frac{3}{2} \log 2 - \frac{3}{2} \log 5}{\log 3 + \log 2 - \log 5}$

$= \frac{\frac{3}{2} \log 3 + \frac{3}{2} \log 2 - \frac{3}{2} \log 5}{\log 3 + \log 2 - \log 5}$

$= \frac{\frac{3}{2} (\log 3 + \log 2 - \log 5)}{\log 3 + \log 2 - \log 5} = \frac{3}{2} (a n s w e r)$

1 year ago

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