Question

Which expression is equivalent to – 2 log2 x + 4 log2 y + 4 log2 z? log base 2 of the quantity x squared y to the fourth all divided by z to the fourth log base 2 of the quantity y to the fourth z to the fourth all divided by x squared log base 2 of the quantity y times z to the fourth all divided by x squared log base 2 of the quantity yz divided by x end quantity raised to the sixth

Answer 1

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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