What is ln(sqrt(x))-1/4 ln(x)+ln(\sqrt[6]{x}) ?

The solution to ln(sqrt(x))-1/4 ln(x)+ln(\sqrt[6]{x}) is ln(x^{5/12})

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simplify ln(sqrt(x))-1/4 ln(x)+ln(\sqrt[6]{x})

simplify

ln (x^{\frac{5}{12}})

Solution steps

Apply log rule:

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

\frac{1}{4} ln (x) = ln (x^{\frac{1}{4}})

Apply log rule:

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

ln (x) - ln (x^{\frac{1}{4}}) = ln (\frac{x}{x ^{\frac{1}{4}}})

Simplify

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

Simplify

= ln (x^{\frac{5}{12}})

lo g_{7} (7 m n^{4})

\frac{ln ( 2 )}{ln ( 3 ) - ln ( 2 )}

\frac{1}{2} lo g_{2} (127)

- lo g_{10} (3.1 \cdot 1 0^{- 5})

lo g_{5} (\frac{5}{7}) + lo g_{5} (\frac{49}{25})

What is ln(sqrt(x))-1/4 ln(x)+ln(\sqrt[6]{x}) ?
The solution to ln(sqrt(x))-1/4 ln(x)+ln(\sqrt[6]{x}) is ln(x^{5/12})