Basic properties of logarithms

Rules for $x,y>0$

$\log_a(xy)=\log_a x+\log_a y$ , $\log_a\dfrac{x}{y}=\log_a x-\log_a y$ , $\log_a(x^m)=m\log_a x$ for $x>0$ . All identities follow from the definition and laws of powers; in equations every logarithm must have a positive argument at the step where you apply a formula.

$\log_a 1=0$ , $\log_a a=1$

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