$\frac{\left (^{5}\textrm{log}\: 10 \right )^{2}-\left ( ^{5}\textrm{log}\: 2 \right )^{2}}{^{5}\textrm{log}\: \sqrt{20}}$ = ....
(A) $\frac{1}{2}$
(B) 1
(C) 2
(D) 4
(E) 5
Pembahasan:
Gunakan $a^{2}-b^{2}=\left ( a+b \right )\left ( a-b \right )$
$\frac{\left (^{5}\textrm{log}\: 10 \right )^{2}-\left ( ^{5}\textrm{log}\: 2 \right )^{2}}{^{5}\textrm{log}\: \sqrt{20}}$
$ =\frac{\left (^{5}\textrm{log}\: 10+\: ^{5}\textrm{log}\: 2 \right )\left ( ^{5}\textrm{log}\: 10-\: ^{5}\textrm{log}\: 2 \right )}{^{5}\textrm{log}\: 20^{\frac{1}{2}}}$
$=\frac{\left (^{5}\textrm{log}\: 10\: \cdot \: 2 \right )\left ( ^{5}\textrm{log}\: \frac{10}{2}\right )}{\frac{1}{2}\: ^{5}\textrm{log}\: 20}$
$=\frac{\left (^{{\color{Red} 5}}\textrm{log}\: {\color{Red} 20} \right )\left ( ^{{\color{Blue} 5}}\textrm{log}\: {\color{Blue} 5}\right )}{\frac{1}{2}\: ^{{\color{Red} 5}}\textrm{log}\: {\color{Red} 20}}$
$=\frac{1}{\frac{1}{2}}$
$=2$
Jawaban __________________________________ (C)
(A) $\frac{1}{2}$
(B) 1
(C) 2
(D) 4
(E) 5
Pembahasan:
Gunakan $a^{2}-b^{2}=\left ( a+b \right )\left ( a-b \right )$
$\frac{\left (^{5}\textrm{log}\: 10 \right )^{2}-\left ( ^{5}\textrm{log}\: 2 \right )^{2}}{^{5}\textrm{log}\: \sqrt{20}}$
$ =\frac{\left (^{5}\textrm{log}\: 10+\: ^{5}\textrm{log}\: 2 \right )\left ( ^{5}\textrm{log}\: 10-\: ^{5}\textrm{log}\: 2 \right )}{^{5}\textrm{log}\: 20^{\frac{1}{2}}}$
$=\frac{\left (^{5}\textrm{log}\: 10\: \cdot \: 2 \right )\left ( ^{5}\textrm{log}\: \frac{10}{2}\right )}{\frac{1}{2}\: ^{5}\textrm{log}\: 20}$
$=\frac{\left (^{{\color{Red} 5}}\textrm{log}\: {\color{Red} 20} \right )\left ( ^{{\color{Blue} 5}}\textrm{log}\: {\color{Blue} 5}\right )}{\frac{1}{2}\: ^{{\color{Red} 5}}\textrm{log}\: {\color{Red} 20}}$
$=\frac{1}{\frac{1}{2}}$
$=2$
Jawaban __________________________________ (C)
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