2log3=a ,maka 3log4+√27log√2+1/3log1/4 Pake caranya guru please

[tex]\log_{2} {3} = a \\ \\ \log_{3} {4} + \log_{\sqrt{27}} {\sqrt{2}} + \log_{\frac{1}{3}} {\frac{1}{4}} \\ = \log_{3} {2^{2}} + \log_{27^{\frac{1}{2}}} {2^{\frac{1}{2}}} + \log_{3^{-1}} {4^{-1}} \\ = 2(\log_{3} {2}) + (\frac{\frac{1}{2}}{\frac{1}{2}})(\log_{27} {2}) + (\frac{-1}{-1}) (\log_{3} {2^{2}}) \\ = 2(\log_{3}{2}) + \frac{1}{3} (\log_{3} {2}) + 2(\log_{3} {2}) \\ = 2(\frac{1}{a}) + \frac{1}{3}(\frac{1}{a}) + 2 (\frac{1}{a}) \\ = \frac{2}{a} + \frac{1}{3a} + \frac{2}{a} \\[/tex]

[tex]= \frac{4}{a} + \frac{1}{3a} \\ = \frac{12}{3a} + \frac{1}{3a} \\ = \frac{13}{3a}[/tex]

2log3 = a ==> log3/log2 = a
3log 4 + V27logV2 + 1/3log 1/4
= log 4/ log 3 + log V2/log V27 +log1/4/log1/3
= log2^2/log3+log2^1/2/log27^1/2+log4^-1/log3^-1.
= 2.log2/log3 +log2^1/2/log(3^3)^1/2 + log(2^2)^-1/ log3^-1
= 2/a + 1/2.log2/(3/2.log3) + -2log2/-1log3
= 2/a + 1/3log2/log3 +2log2/log3
= 2/a +1/3.1/a + 2/a
= 2/a + 1/3a + 2/a
= 6/3a + 1/3 a + 6/3a
= 12/3a
= 4/a