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How can the logarithmic expression be rewritten?

Select True or False for each statement.
(I'm really struggling please help)

How can the logarithmic expression be rewritten? Select True or False for each statement-example-1

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\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( (x)/(y)\right)\implies \log_a(x)-\log_a(y) \end{array} \\\\\\ \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}
\log_3(v)-4\log_3(w)\implies \log_3(v)-\log_3(w^4)\implies \log_3\left( \cfrac{v}{w^4} \right) \\\\[-0.35em] ~\dotfill\\\\ \log_4(n√(m))\implies \log_4(n)+\log_4(√(m)) \\\\\\ \log_4(n)+\log_4\left( m^{(1)/(2)} \right) \implies \log_4(n)+\cfrac{1}{2}\log_4(m)~~\textit{\large \checkmark} \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{cd^3}{e^4} \right)\implies \underline{\log_2(cd^3)}-\log_2(e^4) \\\\\\ \underline{\log_2(c)+\log_2(d^3)}-\log_2(e^4) \implies \log_2(c)+3\log_2(d)-4\log_2(e)

User Kotlet Schabowy
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