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# The function f(x) is defined by f(x)=100−2^x. If f(x)=6, then which of

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Re: The function f(x) is defined by f(x)=100−2^x. If f(x)=6, then which of [#permalink]
Bunuel wrote:
The function f(x) is defined by $$f(x)=100−2^x$$. If f(x)=6, then which of the following is true about the value of x?

A. 0≤x≤4

B. 4<x≤8

C. 8<x≤16

D. 16<x≤32

E. 32<x≤64

f(x) = 6 = 100 - 2^x
2^x = 94
2^6 = 64
and 2^7 = 128
6<x<7

Only B. 4<x≤8 satisfies the criteria

IMO B
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Re: The function f(x) is defined by f(x)=100−2^x. If f(x)=6, then which of [#permalink]
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Given that $$f(x)=100−2^x$$ and f(x)=6 and we need to find the range of values of x

$$f(x)=100−2^x$$ = 6 (given)
=> $$100−2^x = 6$$
=> $$2^x = 100 - 6$$
=> $$2^x = 94$$
Now, we know that $$2^6 = 64$$ and $$2^7 = 128$$
=> x will be between 6 and 7
Only option in that range is 4<x≤8

Hope it helps!

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Re: The function f(x) is defined by f(x)=1002^x. If f(x)=6, then which of [#permalink]
But this does say that x can be 7 or 8. Which is incorrect value of the equation. The correct value is not in the option.
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Re: The function f(x) is defined by f(x)=1002^x. If f(x)=6, then which of [#permalink]
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deepak.brijendra wrote:
But this does say that x can be 7 or 8. Which is incorrect value of the equation. The correct value is not in the option.

Value of x is coming between 6 and 7.
Only the range given in option B where x is between 4 and 8 is containing this range of x is between 6 and 7.
So, that's the correct option choice.

Do you have any other doubt on the same pls?
Re: The function f(x) is defined by f(x)=1002^x. If f(x)=6, then which of [#permalink]
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