Simplify the following :
log 9 - log 3 log 27\dfrac{\text{log 9 - log 3}}{\text{ log 27}} log 27log 9 - log 3
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Given,
⇒log 9 - log 3log 27⇒log 32−log 3log 33⇒2log 3 - log 33log 3⇒log 33log 3⇒13.\Rightarrow \dfrac{\text{log 9 - log 3}}{\text{log 27}} \\[1em] \Rightarrow \dfrac{\text{log 3}^2 - \text{log 3}}{\text{log 3}^3} \\[1em] \Rightarrow \dfrac{\text{2log 3 - log 3}}{\text{3log 3}} \\[1em] \Rightarrow \dfrac{\text{log 3}}{\text{3log 3}} \\[1em] \Rightarrow \dfrac{1}{3}.⇒log 27log 9 - log 3⇒log 33log 32−log 3⇒3log 32log 3 - log 3⇒3log 3log 3⇒31.
Hence, log 9 - log 3log 27=13.\dfrac{\text{log 9 - log 3}}{\text{log 27}} = \dfrac{1}{3}.log 27log 9 - log 3=31.
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log 8 log 9log 27\dfrac{\text{log 8 log 9}}{\text{log 27}}log 27log 8 log 9
log 27log 3\dfrac{\text{log 27}}{\text{log } \sqrt{3}}log 3log 27
Evaluate the following:
log(10÷103)(10 ÷ \sqrt[3]{10})(10÷310)
2 + 12\dfrac{1}{2}21log (10)-3
