How do you expand ${ln (u v^{6})}^{5}$ $ln(uv^6)^5$ ?

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Answer 1 · 2016-09-24T22:55:39

$5 ln u + 30 ln v$ $5lnu+30lnv$

${ln (u v^{6})}^{5}$ $ln(uv^6)^5$

Use log rule ${log x}^{a} = a log x$ $logx^a=alogx$
$5 ln u v^{6}$ $5lnuv^6$

Use log rule $log x y = log x + log y$ $logxy=logx+logy$
$5 (ln u + {ln v}^{6})$ $5(lnu+lnv^6)$

Again use log rule ${log x}^{a} = a log x$ $logx^a=alogx$
$5 (ln u + 6 ln v)$ $5(lnu+6lnv)$

Distribute
$5 ln u + 30 ln v$ $5lnu+30lnv$

OR
${ln (u v^{6})}^{5}$ $ln(uv^6)^5$

Use exponent rule ${(x^{a})}^{b} = x^{a b}$ $(x^a)^b=x^(ab)$
$ln (u^{5} v^{30})$ $ln(u^5v^30)$

Use log rule $log x y = log x + log y$ $logxy=logx+logy$
${ln u}^{5} + {ln v}^{30}$ $lnu^5+lnv^30$

Use log rule ${log x}^{a} = a log x$ $logx^a=alogx$
$5 ln u + 30 ln v$ $5lnu+30lnv$

How do you expand ln(uv6)5ln(uv^6)^5?