Soal

Jika \(x(\log{2}) - y (\log{3}) + z (\log{5}) = 10\), maka \(2x + 8y - 3z = \ldots\)

A. \(-20\)

B. \(-10\)

C. 0

D. 10

E. 20

Jawab

\( \begin{align} x(\log{2}) - y (\log{3}) + z (\log{5}) &= 10\\\\ \log{\dfrac{2^x 5^z}{3^y}} &= \log{10^{10}}\\\\ \dfrac{2^x 5^z}{3^y} &= \dfrac{2^{10} 5^{10}}{3^0} \end{align} \)

Jadi \(x = 10, y = 0, z = 10\), sehingga \(2x + 8y - 3z = 20 + 0 - 30 = -10\)