How do you solve $4^{x} + 4 \geq 21$ $4^x+4>=21$ using a graph?

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How do you solve $4^{x} + 4 \geq 21$ $4^x+4>=21$ using a graph?

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Answer 1 · 2017-03-08T08:36:50

Solution is $x \geq 2.04371$ $x>=2.04371$

Explanation:

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

These are $((-1,-1/2,0,1/2,1,3/2,2,5/2,3),(17/4,9/2,5,6,8,12,20,36,68))$

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 $4^x+4>=21$ 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 $x>=2.04371$ (using MSExcel - Goal seek).

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How do you solve $4^{x} + 4 \geq 21$ $4^x+4>=21$ using a graph?

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