Jawab:
[tex]\begin{aligned}&\bf 3\:\frac{3}{4}=\frac{15}{4}\end{aligned}[/tex]
Penjelasan dengan langkah-langkah:
[tex]\large\text{$\begin{aligned}&\quad\ \frac{{}^3\log25\cdot{}^5\log81-{}^4\log2}{{}^3\log36-{}^3\log4}\\\\&\quad\quad\big[\ \normalsize\text{${}^3\log36-{}^3\log4={}^3\log\tfrac{36}{4}={}^3\log9=2$}\ \big]\\\\&=\frac{{}^3\log25\cdot{}^5\log81-{}^4\log2}{2}\\\\&\quad\quad\big[\ \normalsize\text{${}^4\log2={}^4\log\left(4^{\frac{1}{2}}\right)=\tfrac{1}{2}$}\ \big]\\\\&=\frac{\ {}^3\log25\cdot{}^5\log81-\frac{1}{2}\ }{2}\end{aligned}$}[/tex]
[tex]\large\text{$\begin{aligned}&=\frac{\ {}^3\log\left(5^2\right)\cdot{}^5\log\left(9^2\right)-\frac{1}{2}\ }{2}\\\\&=\frac{\ 2\cdot2\cdot\left({}^3\log5\cdot{}^5\log\9\right)-\frac{1}{2}\ }{2}\\\\&=\frac{\ 4\cdot{}^3\log9-\frac{1}{2}\ }{2}\\\\&=\frac{\ 4\cdot2-\frac{1}{2}\ }{2}\\\\&=\frac{\ 8-\frac{1}{2}\ }{2}\\\\&=4-\tfrac{1}{4}\\\\&=\bf 3\:\tfrac{3}{4}=\tfrac{15}{4}\end{aligned}$}[/tex]
[answer.2.content]
