4 ^ -3 / 4 ^ n = 1/256
What is N?
(i have no idea)
4^-3 / 4^n = 1/256
Now, 256 = 4^4, so that means that 1/256 = 4^-4
so, equating the powers of 4,
-3-n = -4
n = 1
thanks :)
Another approach.
1/4^3*4^n = 1/256,
Invert both sides:
4^3*4^n = 256,
64*4^n = 256,
4^n = 4,
n*Log4 = Log4,
n = Log4/Log4 = 1.
84
6n =
To find the value of n in the equation 4^-3 / 4^n = 1/256, we can begin by simplifying the left side of the equation.
Recall that when we divide two numbers with the same base (in this case, 4), we subtract their exponents. Therefore, 4^-3 / 4^n can be simplified as 4^(-3 - n).
Now, let's rewrite the equation with the simplified left side:
4^(-3 - n) = 1/256
To make it easier to solve, let's express 1/256 as a power of 4.
1/256 can be written as 4^-4 since 4^4 = 256.
So, we can now rewrite the equation as:
4^(-3 - n) = 4^-4
We know that two powers with the same base are equal if and only if their exponents are equal. So, -3 - n = -4.
To solve this equation, let's isolate the variable n.
-3 - n = -4
Adding n to both sides of the equation:
-3 = -4 + n
Next, let's isolate n by adding 4 to both sides:
-3 + 4 = n
1 = n
Therefore, n equals 1.
To summarize, the value of n in the equation 4^-3 / 4^n = 1/256 is 1.