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SIMAK UI 2010

Solusi SIMAK UI 2010 Kode 209 Nomor 12


Jika\ f(x)=\frac{^{3}log\ x}{1-2(^{3}log\ x)}\ maka\ f(x)+f(\frac{3}{x})=....
(A)\quad -3\\(B)\quad -2\\(C)\quad -1\\(D)\quad 1\\(E)\quad 3
Jawaban: C

\begin{array} {lcl} f(x)+f(\frac{3}{x})&=&\frac{^{3}log\ x}{1-2(^{3}log\ x)}+\frac{^{3}log\frac{3}{x}}{1-2(^{3}log\frac{3}{x})} \\\\&=&\frac{^{3}log\ x}{1-2(^{3}log\ x)}+\frac{1-^{3}log\ x}{1-2(1-^{3}log\ x)}\\\\&=&\frac{^{3}log\ x}{1-2(^{3}log\ x)}+\frac{1-^{3}log\ x}{-1+2(^{3}log\ x)}\\\\&=&\frac{^{3}log\ x}{1-2(^{3}log\ x)}-\frac{1-^{3}log\ x}{1-2(^{3}log\ x)}\\\\&=&\frac{-1+2(^{3}log\ x)}{1-2(^{3}log\ x)}\\\\&=&\frac{-\big(1-2(^{3}log\ x)\big)}{1-2(^{3}log\ x)}\\\\&=&-1\end{array}

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