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Sagot :
The expression equivalent to -2log₂x + 4log₂y + 4log₂z is log₂(yz)⁴/x².
To answer the question, we need to know the laws of logarithm
Laws of logarithm
- power law - nlogₐx = logₐxⁿ
- addition law - logₐx + logₐy = logₐxy
Since we want to find the expression equivalent to -2log₂x + 4log₂y + 4log₂z, we simplify using these laws, we have
-2log₂x + 4log₂y + 4log₂z = log₂x⁻² + log₂y⁴ + log₂z⁴ (appying the power law)
= log₂x⁻²y⁴z⁴ (applying the multiplication law)
= log₂y⁴z⁴/x²
= log₂(yz)⁴/x²
So, the expression equivalent to -2log₂x + 4log₂y + 4log₂z is log₂(yz)⁴/x².
Learn more about laws of logarithm here:
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