# Pertidaksamaan Eksponen

### Pertidaksamaan Eksponen

###### Pertidaksamaan Eksponen

Untuk a > 1

\begin{equation*} \begin{split} a^{f(x)} & > a^{g(x)} \\\\ \cancel {a}^{f(x)} & > \cancel {a}^{g(x)} \\\\ f(x) & > g(x) \end{split} \end{equation*}

Untuk a < 1

\begin{equation*} \begin{split} a^{f(x)} & > a^{g(x)} \\\\ \cancel {a}^{f(x)} & > \cancel {a}^{g(x)} \\\\ f(x) & < g(x) \quad {\color {blue} \text{tanda berubah}} \end{split} \end{equation*}

Contoh 01

\begin{equation*}
\begin{split}
(25)^{2x + 1} & \geq (125)^{2x - 4} \\\\
(5^2)^{2x + 1} & \geq (5^3)^{2x - 4} \\\\
5^{4x + 2} & \geq 5^{6x - 12} \\\\
\cancel{5}^{4x + 2} & \geq \cancel{5}^{6x - 12} \\\\
4x + 2 & \geq 6x - 12 \\\\
-2x & \geq -14 \quad {\color {blue} \text{bagi (-2) pada kedua ruas, tanda berubah}}\\\\
x & \leq 7
\end{split}
\end{equation*}

HP = $$\{ x \leq 7 \}$$

Contoh 02

\begin{equation*}
\begin{split}
\left(\frac{1}{11}\right)^{3x-5} & \leq \left(\frac{1}{121}\right)^{x-1} \\\\
\left(\frac{1}{11}\right)^{3x-5} & \leq \left(\left[\frac{1}{11}\right]^2\right)^{x-1} \\\\
\left(\frac{1}{11}\right)^{3x-5} & \leq \left(\frac{1}{11}\right)^{2x - 2} \\\\
\cancel{\left(\frac{1}{11}\right)}^{3x-5} & \leq \cancel{\left(\frac{1}{11}\right)}
^{2x - 2} \\\\
3x-5 & \geq 2x - 2 \quad {\color {blue} \text{tanda berubah}}\\\\
x & \geq 3
\end{split}
\end{equation*}

HP = $$\{ x \geq 3 \}$$