Question

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Find :-
$\frac{ log \sqrt{27} + log \: 8 - log \: \sqrt{1000} }{ log \: 1.2 }$
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Answer 1

Answer:

3/2

Step-by-step explanation:

To Find :-

$\dfrac{\log_{10}{\sqrt{27}}+\log_{10}{8}-\log_{10}{\sqrt{1000}}}{\log_{10}{1.2}}$

Solution  :-

$\dfrac{\log_{10}{\sqrt{27}}+\log_{10}{8}-\log_{10}{\sqrt{1000}}}{\log_{10}{1.2}}$

$=\dfrac{\log_{10}{27^\dfrac{1}{2}}+\log_{10}{2^3}-\log_{10}{1000^{\dfrac{1}{2}}}}{\log_{10}{\dfrac{12}{10}}}$

$=\dfrac{\log_{10}{3^{3\times\dfrac{1}{2}}+3\log_{10}{2}-\log_{10}{10^{3\times\dfrac{1}{2}}}}}{\log_{10}{12}-\log_{10}{10}}$

$=\dfrac{\dfrac{3}{2}\log_{10}{3}+3\log_{10}{2}-\dfrac{3}{2}\log_{10}{10}}{\log_{10}{4}+\log_{10}{3}-1}$

$=\dfrac{\dfrac{3}{2}(\log_{10}{3}+2\log_{10}{2}-1)}{\log_{10}{3}+2\log_{10}{2}-1}$

$=\dfrac{3}{2}$

Used Properties :-

$1)log_{a}{a}=1$

$2)\log_{10}{\dfrac{a}{b}}=\log_{10}{a}-\log_{10}{b}$

Answer 2

Answer:

$3/2</p><p>Step-by-step explanation:</p><p>To Find :-</p><p>\dfrac{\log_{10}{\sqrt{27}}+\log_{10}{8}-\log_{10}{\sqrt{1000}}}{\log_{10}{1.2}}log101.2log1027+log108−log101000</p><p>Solution  :-</p><p>\dfrac{\log_{10}{\sqrt{27}}+\log_{10}{8}-\log_{10}{\sqrt{1000}}}{\log_{10}{1.2}}log101.2log1027+log108−log101000</p><p>=\dfrac{\log_{10}{27^\dfrac{1}{2}}+\log_{10}{2^3}-\log_{10}{1000^{\dfrac{1}{2}}}}{\log_{10}{\dfrac{12}{10}}}=log101012log102721+log1023−log10100021</p><p>=\dfrac{\log_{10}{3^{3\times\dfrac{1}{2}}+3\log_{10}{2}-\log_{10}{10^{3\times\dfrac{1}{2}}}}}{\log_{10}{12}-\log_{10}{10}}=log1012−log1010log1033×21+3log102−log10103×21</p><p>=\dfrac{\dfrac{3}{2}\log_{10}{3}+3\log_{10}{2}-\dfrac{3}{2}\log_{10}{10}}{\log_{10}{4}+\log_{10}{3}-1}=log104+log103−123log103+3log102−23log1010</p><p>=\dfrac{\dfrac{3}{2}(\log_{10}{3}+2\log_{10}{2}-1)}{\log_{10}{3}+2\log_{10}{2}-1}=log103+2log102−123(log103+2log102−1)</p><p>=\dfrac{3}{2}=23</p><p>Used Properties :-</p><p>1)log_{a}{a}=11)logaa=1</p><p>2)\log_{10}{\dfrac{a}{b}}=\log_{10}{a}-\log_{10}{b}2)log10ba=log10a−log10b</p><p>$

I hope it will help you