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2^x+8^f(x)=16 , if f(x) satifies this equation then find range of f(x)

2^x+8^f(x)=16 , if f(x) satifies this equation then find range of f(x)

Grade:11

2 Answers

Vikas TU
14149 Points
4 years ago
Dear student 
2^x+8^f(x)=16
2^x+2^3f(x)=2^4
Take log 
xlog2 + 3f(x)log2 = 4log2
f(x) = (4-x)/3 
X can be from 0 to infinity 
So , range of f(x) will be from (-infinity , 4/3]
Hope this helps 
Aditya Gupta
2081 Points
4 years ago
obviously vikas answer is wrong since logarithm doesnt split up in addition as shown.
in fact, 8^f(x)=16 – 2^x
or f(x)= log8(16 – 2^x)
= log2^3(16 – 2^x)
= 1/3 * log2(16 – 2^x)
now, range of 2^x is (0, inf)
but 16 – 2^x must be greater than 0.
so, 16 – 2^x must lie in (0, 16).
so, log2(16 – 2^x) lies in ( – inf, 4) (as 16= 2^4)
so f(x) = 1/3 * log2(16 – 2^x) lies in ( – inf, 4/3).
kindly approve :=)

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