How do you solve #2^(3x)=64# using a graph?

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Answer 1 · 2017-02-25T09:32:34

The solution is #x=2#

To solve the equation #2^(3x)=64#,

one should draw the graph of #y=2^(3x)-64#

It is apparent that as #x->-oo#, #2^(3x)->0# and #y->-64#

Some other values will be when #x=0# #y=-64#; when #x=1# #y=-56#; when #x=4/3# #y=-48# and when #x=5/3# #y=-32#

and graph appears as follows:
graph{2^(3x)-64 [-4, 4, -75, 75]}

As the graph intersects #x#-axis at #(2,0)#

the solution is #x=2#