What is ln(sqrt(x))-1/3 ln(x)+ln(\sqrt[6]{x}) ?

The solution to ln(sqrt(x))-1/3 ln(x)+ln(\sqrt[6]{x}) is 2ln(\sqrt[6]{x})

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simplify ln(sqrt(x))-1/3 ln(x)+ln(\sqrt[6]{x})

simplify

Solution steps

Apply log rule:

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

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

Apply log rule:

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

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

Simplify

Add similar elements:

lo g_{10} (\frac{x ^{2} - c ^{2}}{2}) - lo g_{10} (x - c)

2 ln (3) - \frac{1}{2} ln (2) + \frac{π}{12}

lo g_{10} (\frac{x ^{2}}{7})

lo g_{5} (\frac{25}{x + 5})

lo g_{2} (\frac{3 y}{z})

What is ln(sqrt(x))-1/3 ln(x)+ln(\sqrt[6]{x}) ?
The solution to ln(sqrt(x))-1/3 ln(x)+ln(\sqrt[6]{x}) is 2ln(\sqrt[6]{x})