# How do you solve 4^x+4>=21 using a graph?

Mar 8, 2017

Solution is $x \ge 2.04371$

#### Explanation:

To solve ${4}^{x} + 4 \ge 21$ using a graph, first let us create a graph by choosing different values of $x$ say $- 1$, $- \frac{1}{2}$, $0$, $\frac{1}{2}$, $1$, $\frac{3}{2}$, $2$, $\frac{5}{2}$, $3$ and corresponding values of ${4}^{x} + 4$.

These are $\left(\begin{matrix}- 1 & - \frac{1}{2} & 0 & \frac{1}{2} & 1 & \frac{3}{2} & 2 & \frac{5}{2} & 3 \\ \frac{17}{4} & \frac{9}{2} & 5 & 6 & 8 & 12 & 20 & 36 & 68\end{matrix}\right)$

and graph appears as follows:
graph{4^x+4 [-1, 3, -5, 30]}

As is observed by zooming the graph near the place, where ${4}^{x} + 4$ crosses $y = 21$ and we find that ${4}^{x} + 4 \ge 21$ for some $x$ greater than $2$, say around $2.04$.

graph{4^x+4 [1.68, 2.18, 16.944, 21.32]}

Actually solution is $x \ge 2.04371$ (using MSExcel - Goal seek).