Evaluate the following without using log tables :
log 9−log 3log 27\dfrac{\log \space 9 - \log \space 3}{\log \space 27}log 27log 9−log 3
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Given,
⇒log 9−log 3log 27⇒log 93log 33⇒log 33log 3⇒13.\Rightarrow \dfrac{\log \space 9 - \log \space 3}{\log \space 27} \\[1em] \Rightarrow \dfrac{\log \space {\dfrac{9}{3}}}{\log \space 3^3} \\[1em] \Rightarrow \dfrac{\log \space 3}{3\log \space 3} \\[1em] \Rightarrow \dfrac{1}{3}.⇒log 27log 9−log 3⇒log 33log 39⇒3log 3log 3⇒31.
Hence, log 9−log 3log 27=13\dfrac{\log \space 9 - \log \space 3}{\log \space 27} = \dfrac{1}{3}log 27log 9−log 3=31.
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log 128log 32\dfrac{\log \space 128}{\log \space 32}log 32log 128
log 27log 3\dfrac{\log \space 27}{\log \space \sqrt{3}}log 3log 27
Given : log 2 = 0.3010 and log 3 = 0.4771, find the value of :
(i) log 12
(ii) log 25
(iii) log 18\log \space \sqrt{18}log 18
(iv) log (94)\log \space \Big(\dfrac{9}{4}\Big)log (49)
If log 2 = 0.3010, find the value of (log 7516−2log 59+log 32243)\Big(\log \space \dfrac{75}{16} - 2 \log \space \dfrac{5}{9} + \log \space \dfrac{32}{243}\Big)(log 1675−2log 95+log 24332)
