Simplify the following :
log 27log 3\dfrac{\text{log 27}}{\text{log } \sqrt{3}}log 3log 27
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Given,
⇒log 27log 3⇒log 33log 312⇒3log 312log 3⇒312⇒6.\Rightarrow \dfrac{\text{log 27}}{\text{log }\sqrt{3}} \\[1em] \Rightarrow \dfrac{\text{log 3}^3}{\text{log 3}^{\dfrac{1}{2}}} \\[1em] \Rightarrow \dfrac{\text{3log 3}}{\dfrac{1}{2}\text{log 3}} \\[1em] \Rightarrow \dfrac{3}{\dfrac{1}{2}} \\[1em] \Rightarrow 6.⇒log 3log 27⇒log 321log 33⇒21log 33log 3⇒213⇒6.
Hence, log 27log 3\dfrac{\text{log 27}}{\text{log }\sqrt{3}}log 3log 27 = 6.
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log4log2\dfrac{\text{log} 4}{\text{log} 2}log2log4
log 8 log 9log 27\dfrac{\text{log 8 log 9}}{\text{log 27}}log 27log 8 log 9
log 9 - log 3 log 27\dfrac{\text{log 9 - log 3}}{\text{ log 27}} log 27log 9 - log 3
Evaluate the following:
log(10÷103)(10 ÷ \sqrt[3]{10})(10÷310)
