[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 rationals}
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log_a\left( \frac{x}{y}\right)\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)\\\\
------------------------------- [/tex]
[tex] \bf 2log_5(x)-log_5(2)+log_5(x)\implies {\stackrel{\textit{of exponentials}}{log_5(x^2)}-log_5(2)}+log_5(x)
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\stackrel{\textit{\textit{of rationals}}}{log_5\left( \cfrac{x^2}{2} \right)}+log_5(x)\implies \stackrel{\textit{of factors}}{log_5\left(\cfrac{x^2}{2}\cdot x \right)}\implies log_5\left( \cfrac{x^3}{2} \right) [/tex]
