The given expression is log4(xy^4z^4).

Using the properties of logarithms, we can expand this expression as follows:

Step 1: Apply the property logb(mn) = logb(m) + logb(n) to separate the terms inside the logarithm.

log4(xy^4z^4) = log4(x) + log4(y^4z^4)

Step 2: Repeat the process for the second term.

log4(x) + log4(y^4z^4) = log4(x) + log4(y^4) + log4(z^4)

Step 3: Apply the property logb(m^n) = n*logb(m) to simplify the expression.

log4(x) + log4(y^4) + log4(z^4) = log4(x) + 4*log4(y) + 4*log4(z)

So, the expanded form of the given expression is log4(x) + 4*log4(y) + 4*log4(z).

Question

The given expression is log4(xy^4z^4).

Using the properties of logarithms, we can expand this expression as follows:

Step 1: Apply the property logb(mn) = logb(m) + logb(n) to separate the terms inside the logarithm.

log4(xy^4z^4) = log4(x) + log4(y^4z^4)

Step 2: Repeat the process for the second term.

log4(x) + log4(y^4z^4) = log4(x) + log4(y^4) + log4(z^4)

Step 3: Apply the property logb(m^n) = n*logb(m) to simplify the expression.

log4(x) + log4(y^4) + log4(z^4) = log4(x) + 4*log4(y) + 4*log4(z)

So, the expanded form of the given expression is log4(x) + 4*log4(y) + 4*log4(z).

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