Laws of logarithms

logbx=y⇔by=x ${log}_{b} x = y \Leftrightarrow b^{y} = x$
logb(xy)=logbx+logby ${log}_{b} (x y) = {log}_{b} x + {log}_{b} y$
logbyx=logbx−logby ${log}_{b} \frac{x}{y} = {log}_{b} x - {log}_{b} y$
logbxn=nlogbx ${log}_{b} x^{n} = n {log}_{b} x$
logbx=logkblogkx ${log}_{b} x = \frac{{log}_{k} x}{{log}_{k} b}$
blogbx=x $b^{{log}_{b} x} = x$
logx=log10x, lnx=logex $log x = {log}_{10} x, ln x = {log}_{e} x$

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