Evaluate the following without using log tables :
log 128log 32\dfrac{\log \space 128}{\log \space 32}log 32log 128
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Given,
⇒log 128log 32⇒log 27log 25⇒7log 25log 2⇒75.\Rightarrow \dfrac{\log \space 128}{\log \space 32} \\[1em] \Rightarrow \dfrac{\log \space 2^7}{\log \space 2^5} \\[1em] \Rightarrow \dfrac{7\log \space 2}{5\log \space 2} \\[1em] \Rightarrow \dfrac{7}{5}.⇒log 32log 128⇒log 25log 27⇒5log 27log 2⇒57.
Hence, log 128log 32=75\dfrac{\log \space 128}{\log \space 32} = \dfrac{7}{5}log 32log 128=57.
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Express the following as a single logarithm :
1−13log10 641 − \dfrac{1}{3} \log_{10} \space 641−31log10 64
log 81log 27\dfrac{\log \space 81}{\log \space 27}log 27log 81
log 27log 3\dfrac{\log \space 27}{\log \space \sqrt{3}}log 3log 27
log 9−log 3log 27\dfrac{\log \space 9 - \log \space 3}{\log \space 27}log 27log 9−log 3
