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}

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