Solve the inequality : (0.25)^(x-4)=<(1/16)^x.

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We have to solve: (0.25)^(x-4)=<(1/16)^x

(0.25)^(x-4)=<(1/16)^x

=> (1/4)^(x- 4) =< (1/16)^x

=> (1/4)^(x- 4) =< (1/4)^2x

As (1/4) is less than 1, we have 1/ 4 > (1/4^2)

Similarly, we can say (x- 4) => 2x

=> x - 2x => 4

=> -x => 4

=> x =< -4

Therefore x <= -4.

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giorgiana1976 | Student

We'll transform the decimal form of 0.25 into a fraction:

0.25 = 25/100 = 1/4

We notice that 1/16 = 1/4^2

We'll re-write the inequality:

(1/4)^(x-4) =< (1/4)^2x

Since the bases are below unit, the exponential function is decreasing and we'll get:

x-4 >= 2x

We'll subtract 2x:

x - 2x - 4 >= 0

-x - 4 > = 0

-x >= 4

x =< -4

The range of values of x, that make the inequality to hold, is:

(-infinite ; -4]

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