Questions: y = log4 256

Solution Steps

To solve the equation \( y = \log_{4} 256 \), we need to find the value of \( y \) such that \( 4^y = 256 \). We can use the change of base formula for logarithms to convert the base 4 logarithm to a base 10 or base \( e \) logarithm, which can be computed using Python's math library.

1. Use the change of base formula: \( \log_{4} 256 = \frac{\log_{10} 256}{\log_{10} 4} \).
2. Compute the logarithms using Python's math library.

We start with the equation \( y = \log_{4} 256 \). This means we are looking for the exponent \( y \) such that \( 4^y = 256 \).

Next, we can express \( 256 \) as a power of \( 4 \). We know that \( 256 = 4^4 \) because \( 4^4 = 256 \).

From the equation \( 4^y = 256 \), we can substitute \( 256 \) with \( 4^4 \): \[ 4^y = 4^4 \] Since the bases are the same, we can equate the exponents: \[ y = 4 \]

Final Answer