Answer:
The value of x is 11.
Step-by-step explanation:
Consider the provided information.
It is given that [tex]3^x = 27 mod\ 32 [/tex]
We know that:
[tex]3^4=81[/tex]
Now if we divide the number 81 with 32 it will gives us remainder 17.
This can be written as:
[tex]3^4\equiv 17(mod\ 32)[/tex]
Now use the property: [tex]a^n\equiv b^n(mod\ m)[/tex]
[tex](3^4)^2\equiv 17^2(mod\ 32)[/tex]
17²=289, if we divide 289 with 32 it will gives us remainder 1, thus.
[tex]3^8\equiv 1(mod\ 32)[/tex]
Multiply both the sides by 3³.
[tex]3^8\times 3^3\equiv 3^3(mod\ 32)[/tex]
[tex]3^{11}\equiv 27(mod\ 32)[/tex]
Hence, the value of x is 11.
