Solve inequality 0.2^x>0.4?

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Define a function

`f(x)=.2^x-.4`

Let us draw its graph

From graph we can conclude that f(x) is positive at (x=0) and negative at (x=1) . f is continuous function changes its sign between 0 and 1. Thus there exist a point in between 0 and 1 where f(x)=0

From graph ,let estimate the point

`f(.8)=.2^(.8)-.4=-0.12`

`f(.7)=.2^(.7)-.4=-.076`

`f(.6)=.2^.6-.4=-.019`

`f(.5)=.2^(.5)-.4=.047`

f(.6) s negative and f(.5) is positive

Thus by bisection method x=.55 is point where f(x)=0

Thus solution of the problem is

-oo < x <=.55

( minus infinity is less than x is less than or equals to .55 )

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