SBMPTN Zone : Fungsi Eksponen

Berikut ini adalah kumpulan soal mengenai Fungsi Eksponen tingkat SBMPTN. Jika ada jawaban yang salah, mohon dikoreksi melalui komentar. Terima kasih.

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No. 1

Diketahui ${f(x) = 2^{5-x} + 2^x-12}$. Jika ${f\left(x_1\right) =f\left(x_2\right) = 0}$ maka $x_1\cdot x_2 =$

1. $-6$
2. $-5$
3. $4$

4. $5$
5. $6$

Ganesha Operation

$\begin{array}{rl}f(x)& =0\\ 2^{5-x}+2^x-12& =0\\ {\displaystyle \frac{2^5}{2^x}}+2^x-12& =0\\ {\displaystyle \frac{32}{2^x}}+2^x-12& =0& \times 2^x\\ 32+{\left(2^x\right)}^2-12\cdot 2^x& =0\\ {\left(2^x\right)}^2-12\cdot 2^x+32& =0\end{array}$
Misal ${2^x=p}$
$\begin{array}{rl}{p}^2-12p+32& =0\\ (p-4)(p-8)& =0\end{array}$

• $p_1=4$
  $\begin{array}{rl}{2}^{x_1}& =4\\ 2^{x_1}& =2^2\\ x_1=2\end{array}$
• $p_2=8$
  $\begin{array}{rl}{2}^{x_2}& =8\\ 2^{x_2}& =2^3\\ x_2& =3\end{array}$

${x_1\cdot x_2=2\cdot3=\boxed{\boxed{6}}}$

Jadi, $x_1\cdot x_2 =6$.
JAWAB: E

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