Jika $9^n=4$ maka $4.3^{n+1}-27^n=...$
A. 8
B. 12
C. 16
D. 18
E. 24
Pembahasan:
$\begin{align}9^n&=4\\ (3^2)^n&=2^2\\ 3^n&=2 \end{align}$
maka:
$\begin{align}4.3^{n+1}-27^n&=4.3^n.3-(3^3)^n\\ &=12.3^n-(3^n)^3\\ &=12.2-2^3\\ &=16 \end{align}$
Sumber http://www.catatanmatematika.comA. 8
B. 12
C. 16
D. 18
E. 24
Pembahasan:
$\begin{align}9^n&=4\\ (3^2)^n&=2^2\\ 3^n&=2 \end{align}$
maka:
$\begin{align}4.3^{n+1}-27^n&=4.3^n.3-(3^3)^n\\ &=12.3^n-(3^n)^3\\ &=12.2-2^3\\ &=16 \end{align}$
Kunci: C. 16