How do you use the properties of logarithms to rewrite(expand) each logarithmic expression ${log}_{b} (y z^{6}))$ $log_b(yz^6))$ ?

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Answer 1 · 2018-03-03T11:38:21

${log}_{b} (y) + 6 {log}_{b} (z)$ $log_b(y)+6log_b(z)$

From the laws of logarithms:

$log (a b) = log (a) + log (b)$ $color(red)bb(log(ab)=log(a)+log(b))$

$log (b^{a}) = a log (b)$ $color(red)bb(log(b^a)=alog(b))$

${log}_{b} (y z^{6}) = {log}_{b} (y) + {log}_{b} (z^{6}) \Rightarrow$ $log_b(yz^6)=log_b(y)+log_b(z^6)=>$

${log}_{b} (y) + 6 {log}_{b} (z)$ $log_b(y)+6log_b(z)$

How do you use the properties of logarithms to rewrite(expand) each logarithmic expression logb(yz6))log_b(yz^6))?