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SMK Teknologi dan Rekayasa

Soal 16 Logaritma


Jika\ log 2=x,\ log 3=y,\ log 5=z,\ maka\ log 1500\ jika\ dinyatakan\\dalam\ x,\ y,\ z\ adalah\ ....\\a. \ \ x + y + z\ \ \ \ \ \ \ \ b. \ \ x + 2y + 3z\ \ \ \ \ \ c. \ \ 2x + y + 3z\ \ \ \ \ \ \ \ d. \ \ 3x + y + 2z\ \ \ \ \ \ \ \ e. \ \ 2x + y + z
Jawaban: c

\begin{array}{rcl}log 1500&=&log (100\times 15)\\\\&=&\ log (4\times 25\times 3\times 5)\\\\&=&log (2^{2}\times 3\times 5^{3})\\\\&=&log 2^{2}+log 3+log 5^{3}\\\\&=&2.log 2+log 3+3.log 5\\\\&=&2x+y+3z\end{array}

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