How do you solve the exponential inequality #9^(2x-3)<=9^(x+2)#?

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Answer 1 · 2017-12-14T12:42:05

#x<=5#

#9^(2x-3) <= 9^(x+2)#

#=>2x-3 <= x+2#

#=>(2x-3) - (x+2) <= 0#

#=>x-5 <= 0#

#=>x <= 5#

So, we see that it's true for all the values of #x# where #x# is either less or equal to #5#.

Visually, all the shaded region in the graph below.

graph{x<=5}