Question

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

Answer 1

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.