Question 36

If $$4^{(x+y)} = 256$$ and $$(256)^{(x-y)} = 4$$, then what is the value of x and y?

Solution

Given : $$4^{(x+y)} = 256$$

=> $$4^{(x+y)} = 4^4$$

=> $$(x+y)=4$$ ----------(i)

Similarly, $$(256)^{(x-y)} = 4$$

=> $$4^{4(x-y)}=4^1$$

=> $$(x-y)=\frac{1}{4}$$ --------(ii)

Adding equations (i) and (ii), we get :

=> $$2x=4+\frac{1}{4}=\frac{17}{4}$$

=> $$x=\frac{17}{8}$$

Substituting it in equation (i), => $$y=4-\frac{17}{8}=\frac{32-17}{8}$$

=> $$y=\frac{15}{8}$$

=> Ans - (A)

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