Evaluate the following without using log tables :
log 81log 27\dfrac{\log \space 81}{\log \space 27}log 27log 81
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Given,
⇒log 81log 27⇒log 34log 33⇒4log 33log 3⇒43.\Rightarrow \dfrac{\log \space 81}{\log \space 27} \\[1em] \Rightarrow \dfrac{\log \space 3^4}{\log \space 3^3} \\[1em] \Rightarrow \dfrac{4\log \space 3}{3\log \space 3} \\[1em] \Rightarrow \dfrac{4}{3}.⇒log 27log 81⇒log 33log 34⇒3log 34log 3⇒34.
Hence, log 81log 27=43\dfrac{\log \space 81}{\log \space 27} = \dfrac{4}{3}log 27log 81=34.
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Express the following as a single logarithm :
2log10 (1113)+log10 (13077)−log10 (5591)2 \log{10} \space \Big(\dfrac{11}{13}\Big) + \log{10} \space \Big(\dfrac{130}{77}\Big) − \log_{10} \space \Big(\dfrac{55}{91}\Big)2log10 (1311)+log10 (77130)−log10 (9155)
1−13log10 641 − \dfrac{1}{3} \log_{10} \space 641−31log10 64
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
