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

```							Dear student 2^x+8^f(x)=162^x+2^3f(x)=2^4Take log xlog2 + 3f(x)log2 = 4log2f(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
```
4 months ago
```							obviously vikas answer is wrong since logarithm doesnt split up in addition as shown.in fact, 8^f(x)=16 – 2^xor 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 :=)
```
4 months ago
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