What is 1/3 ln(6x^2)+ln(3x) ?

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

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simplify 1/3 ln(6x^2)+ln(3x)

simplify

\frac{1}{3} ln (6 x^{2}) + ln (3 x)

Solution steps

\frac{1}{3} ln (6 x^{2}) + ln (3 x)

Apply log rule:

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

\frac{1}{3} ln (6 x^{2}) = ln ((6 x^{2})^{\frac{1}{3}})

= ln ((6 x^{2})^{\frac{1}{3}}) + ln (3 x)

Apply log rule:

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

ln ((6 x^{2})^{\frac{1}{3}}) + ln (3 x) = ln (3 x (6 x^{2})^{\frac{1}{3}})

= ln (3 x (6 x^{2})^{\frac{1}{3}})

5 ln (\frac{H - 5}{H + 3})

\frac{1}{2} ln (\frac{0.7}{0.3})

ln (0.66666666 x^{1.5})

ln (\frac{15}{11})

- lo g_{10} (5.512 \cdot 1 0^{- 11})

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