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

1 Answer
Shwetank Mauria
Mar 8, 2017

Solution is #x>=2.04371#

Explanation:

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