HOTS Zone : Eksponen (pangkat) [3]
Table of Contents
Tipe
No.
\[2^a+2^b+2^c=\dfrac{35}{32}\] $a$, $b$, $c$ bilangan bulat. Tentukan nilai $a+b+c$.ALTERNATIF PENYELESAIAN
\(\begin{aligned}
2^a+2^b+2^c&=\dfrac{35}{32}\\[4pt]
&=\dfrac{32+2+1}{32}\\[4pt]
&=\dfrac{32}{32}+\dfrac{2}{32}+\dfrac{1}{32}\\[4pt]
&=1+\dfrac1{16}+\dfrac{1}{32}\\[4pt]
&=2^0+\dfrac1{2^4}+\dfrac{1}{2^5}\\[4pt]
&=2^0+2^{-4}+2^{-5}
\end{aligned}\)
\(\begin{aligned} a+b+c&=0+(-4)+(-5)\\ &=\color{blue}\boxed{\boxed{\color{black}-9}} \end{aligned}\)
\(\begin{aligned} a+b+c&=0+(-4)+(-5)\\ &=\color{blue}\boxed{\boxed{\color{black}-9}} \end{aligned}\)
Jadi, $a+b+c=-9$.
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