Simplify Complex Logarithmic Expression Using Log Laws

00:00 4 marks

Simplify the expression using the logarithmic laws:

$ \log\left(\frac{(2x^2y)^3 \sqrt{z}}{4xy^2z^3} \right) $

Express your answer as a sum and/or difference of logarithms.

Hint Hint

Hint

Expand the powers and simplify the algebraic fraction before applying the logarithm rules.

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Complete Answer

$ \log(2) + 5\log(x) + \log(y) – \frac{5}{2}\log(z) $

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