[tex]\bf \textit{logarithm of factors}
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log_a(xy)\implies log_a(x)+log_a(y)
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\textit{Logarithm of exponentials}
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log_a\left( x^b \right)\implies b\cdot log_a(x)\\\\
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2log_5(5x^3)+\cfrac{1}{3}log_5(x^2+6)\implies log_5[~~(5x^3)^2~~]+log_5[~~(x^2+6)^{\frac{1}{3}}~~]
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log[~(5^2x^{3\cdot 2})~]+log_5[~\sqrt[3]{x^2+6}~]\implies log[~(25x^6)~]+log_5[~\sqrt[3]{x^2+6}~]
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log_5[~~(25x^6)(\sqrt[3]{x^2+6})~~]\implies log_5(25x^6\sqrt[3]{x^2+6})[/tex]
