Solve inequality 0.2^x>0.4?

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Define a function


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(.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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