How do you condense $\frac{1}{3} ln x + ln y$ $1/3ln x + ln y$ ?

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Answer 1 · 2016-04-14T08:25:56

$\frac{1}{3} ln x + ln y = ln (y \sqrt[3]{x})$ $1/3lnx+lny=ln(yroot(3)x)$

We can condense using identities

$log_ap_1+log_ap_2+log_ap_3+..+log_ap_n=log_a(p_1*p_2*p_3*...*p_n)$

and $nlog_ap=log_ap^n$ and

$1/mlog_ap=log_ap^(1/m)=log_aroot(m)p$

Using these $1/3lnx+lny=lnroot(3)x+lny=ln(yroot(3)x)$

How do you condense 1/3ln x + ln y13lnx+lny1/3ln x + ln y?