Soal

Jika [latex]x(\log{2}) – y (\log{3}) + z (\log{5}) = 10[/latex], maka [latex]2x + 8y – 3z = \ldots[/latex]

A. [latex]-20[/latex]

B. [latex]-10[/latex]

C. 0

D. 10

E. 20

Jawab

[latex] \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} [/latex]

Jadi [latex]x = 10, y = 0, z = 10[/latex], sehingga [latex]2x + 8y – 3z = 20 + 0 – 30 = -10[/latex]