What is 1/3 ln(x)-7ln(y)+(ln(z))/2 ?

The solution to 1/3 ln(x)-7ln(y)+(ln(z))/2 is ln((x^{1/3}}{y^7})+\frac{ln(z))/2

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simplify 1/3 ln(x)-7ln(y)+(ln(z))/2

simplify

\frac{1}{3} ln (x) - 7 ln (y) + \frac{ln ( z )}{2}

ln (\frac{x ^{\frac{1}{3}}}{y ^{7}}) + \frac{ln ( z )}{2}

Solution steps

\frac{1}{3} ln (x) - 7 ln (y) + \frac{ln ( z )}{2}

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{3} ln (x) = ln (x^{\frac{1}{3}})

= ln (x^{\frac{1}{3}}) - 7 ln (y) + \frac{ln ( z )}{2}

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

7 ln (y) = ln (y^{7})

= ln (x^{\frac{1}{3}}) - ln (y^{7}) + \frac{ln ( z )}{2}

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (x^{\frac{1}{3}}) - ln (y^{7}) = ln (\frac{x ^{\frac{1}{3}}}{y ^{7}})

= ln (\frac{x ^{\frac{1}{3}}}{y ^{7}}) + \frac{ln ( z )}{2}

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What is 1/3 ln(x)-7ln(y)+(ln(z))/2 ?
The solution to 1/3 ln(x)-7ln(y)+(ln(z))/2 is ln((x^{1/3}}{y^7})+\frac{ln(z))/2