Final answer:
To express y in terms of x from the equation log₄1 + log₄x - log₄y = 2, we use logarithm properties to simplify and solve, resulting in y = x/16.
Step-by-step explanation:
The equation given is log₄1 + log₄x - log₄y = 2. To express y in terms of x, we need to use the properties of logarithms. By using the property that logb(a) - logb(c) = logb(a/c), we can combine the logs on one side.
Firstly, we can eliminate log₄1 because the logarithm of 1 in any base is 0. So the equation simplifies to log₄x - log₄y = 2. Now we apply the subtraction property of logarithms, which gives us log₄(x/y) = 2. To remove the logarithm, we can exponentiate both sides with the base of the logarithm. So 4² = x/y, which means 16 = x/y. Therefore, to express y in terms of x, we can multiply both sides by y and then divide both sides by 16, which gives us y = x/16.