Write the expression as a sum or difference of logarithms. Log_b(x²y^-4) A) 2log_bx +4log_by B) 2log_bx -4log_by C) -4log_bx -2log_by D) -8log_b(xy)

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Quizplus · Accepted Answer

The expression can be rewritten using the properties of logarithms: $\log_b(x^2y^{-4}) = 2\log_b(x) - 4\log_b(y)$, which matches choice B. This uses the power rule $\log_b(x^m) = m\log_b(x)$ and the quotient rule $\log_b(\frac{x}{y}) = \log_b(x) - \log_b(y)$.

Write the Expression as a Sum or Difference of Logarithms