If 451 in base6 - P in base7 = 301 in base6, find d. value of P

451 base 6

1*6^0 + 5*6^1 + 4*6^2
= 1 + 30 + 144
= 175 in base 10

301 base 6
1*10^0 + 0*6^1 + 3*6^2
= 1 + 0 + 108
= 109 in base 10

so in base 10
175 - x = 109
x = 66 in base 10
put that in base 7
7^2 = 49
17 left
2*7^1 = 14
3 left
so
1^7^2 + 2*7^1 + 3*7^0
or
P = 123 in base 7

By the way, I just did that by common sense. I do not know what routine you are really supposed to know. You may have a better way to shift back and forth.

301 base 6

1*10^0 + 0*6^1 + 3*6^2
should be
301 base 6
1*6^0 + 0*6^1 + 3*6^2
= 109

You could just do the subtraction in base 6 and then convert the answer to base 7:

451-301 = 150
1506 = 1237

good point :)

To solve this problem, we need to convert the numbers given in different bases to a common base, in this case, base 10, in order to perform the subtraction and find the value of P.

Let's start by converting 451 in base 6 to base 10.
451 in base 6 can be rewritten as (4 * 6^2) + (5 * 6^1) + (1 * 6^0) = 172 in base 10.

Next, let's convert 301 in base 6 to base 10.
301 in base 6 can be rewritten as (3 * 6^2) + (0 * 6^1) + (1 * 6^0) = 109 in base 10.

Now, let's convert P in base 7 to base 10.
Since P represents an unknown value, we'll use a variable to represent it. Let's use the variable P itself.
So, P in base 7 can be written as (P * 7^0) = P in base 10.

Now, let's write the equation using the converted values:
172 - P + (P * 7^0) = 109

Simplifying the equation:
172 - P + P = 109
P cancels out, and we are left with:
172 = 109

This equation is not true, which means there is no value of P that satisfies the equation. Therefore, there is no value of P that can be determined in this case.