Simplify the following :
log 8 log 9log 27\dfrac{\text{log 8 log 9}}{\text{log 27}}log 27log 8 log 9
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Given,
⇒log 8 log 9log 27⇒log 23log 32log 33⇒3log 2. 2log 33log3⇒6log 2.log 33log 3⇒2log 2=log 22=log 4.\Rightarrow \dfrac{\text{log 8 log 9}}{\text{log 27}} \\[1em] \Rightarrow \dfrac{\text{log 2}^3 \text{log 3}^2}{\text{log 3}^3} \\[1em] \Rightarrow \dfrac{\text{3log 2. 2log 3}}{3\text{log} 3} \\[1em] \Rightarrow \dfrac{\text{6log 2.log 3}}{\text{3log 3}} \\[1em] \Rightarrow 2\text{log 2} = \text{log 2}^2 \\[1em] = \text{log 4}.⇒log 27log 8 log 9⇒log 33log 23log 32⇒3log33log 2. 2log 3⇒3log 36log 2.log 3⇒2log 2=log 22=log 4.
Hence, log 8 log 9log 27\dfrac{\text{log 8 log 9}}{\text{log 27}}log 27log 8 log 9 = log 4.
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log a3 ÷ log a2
log4log2\dfrac{\text{log} 4}{\text{log} 2}log2log4
log 27log 3\dfrac{\text{log 27}}{\text{log } \sqrt{3}}log 3log 27
log 9 - log 3 log 27\dfrac{\text{log 9 - log 3}}{\text{ log 27}} log 27log 9 - log 3
