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White raven [17]
3 years ago
13

Find x such that 3^x = 27 mod 32 (b)

Mathematics
1 answer:
gregori [183]3 years ago
7 0

Answer:

The value of x is 11.

Step-by-step explanation:

Consider the provided information.

It is given that 3^x = 27 mod\ 32

We know that:

3^4=81

Now if we divide the number 81 with 32 it will gives us remainder 17.

This can be written as:

3^4\equiv 17(mod\ 32)

Now use the property: a^n\equiv b^n(mod\ m)

(3^4)^2\equiv 17^2(mod\ 32)

17²=289, if we divide 289 with 32 it will gives us remainder 1, thus.

3^8\equiv 1(mod\ 32)

Multiply both the sides by 3³.

3^8\times 3^3\equiv 3^3(mod\ 32)

3^{11}\equiv 27(mod\ 32)

Hence, the value of x is 11.

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4) find n(x) in the interval B,C
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5) find h(x) = n(m(x)) in the interval A,B
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h(x)=(18/25)x+18
find h'(x) 
h'(x)=18/25=0.72 

for the interval (A,B) h'(x)=-1.44
for the interval (B,C) h'(x)= 0.72

<span> h'(x) = 1.44 ------------ > not exist</span>

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