Evaluate the following without using log tables :
log 27log 3\dfrac{\log \space 27}{\log \space \sqrt{3}}log 3log 27
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Given,
⇒log 27log 3⇒log 33log 312⇒3log 312log 3⇒312⇒3×2⇒6.\Rightarrow \dfrac{\log \space 27}{\log \space \sqrt{3}} \\[1em] \Rightarrow \dfrac{\log \space 3^3}{\log \space {3}^{\dfrac{1}{2}}} \\[1em] \Rightarrow \dfrac{3\log \space 3}{{\dfrac{1}{2}}\log \space 3} \\[1em] \Rightarrow \dfrac{3}{{\dfrac{1}{2}}} \\[1em] \Rightarrow 3 \times 2 \\[1em] \Rightarrow 6.⇒log 3log 27⇒log 321log 33⇒21log 33log 3⇒213⇒3×2⇒6.
Hence, log 27log 3\dfrac{\log \space 27}{\log \space \sqrt{3}}log 3log 27 = 6.
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log 81log 27\dfrac{\log \space 81}{\log \space 27}log 27log 81
log 128log 32\dfrac{\log \space 128}{\log \space 32}log 32log 128
log 9−log 3log 27\dfrac{\log \space 9 - \log \space 3}{\log \space 27}log 27log 9−log 3
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)
