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SMUP 2010

Solusi SMUP 2010 Kode 041 – Nomor 6


\frac{\big(^{5}log10\big)^2-\big(^{5}log2\big)^2}{^{5}log\sqrt{20}}=....
A.\quad \frac{1}{2}\\B.\quad 1\\C.\quad 2\\D.\quad 4\\E.\quad 5
Jawaban: C

\begin{array} {rcl} \frac{\big(^{5}log10\big)^2-\big(^{5}log2\big)^2}{^{5}log\sqrt{20}}&=&\frac{\big(^{5}log10-^{5}log2\big)\big(^{5}log10+^{5}log2\big)}{^{5}log\sqrt{20}}\\\\&=&\frac{^{5}log5\:\:\: \times \:\:\: ^{5}log20}{^{5}log\sqrt{20}}\\\\&=&\frac{^{5}log20}{^{5}log\sqrt{20}}\\\\&=&^{\sqrt{20}}log20\\\\&=&\frac{1}{\frac{1}{2}}\\\\&=&2\end{array}

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