What is ln(14)-2/3 ln(3x)-4/3 ln(4-3x) ?

The solution to ln(14)-2/3 ln(3x)-4/3 ln(4-3x) is ln((14\sqrt[3]{3}\sqrt[3]{x})/(3x(4-3x)^{4/3)})

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simplify ln(14)-2/3 ln(3x)-4/3 ln(4-3x)

simplify

ln (14) - \frac{2}{3} ln (3 x) - \frac{4}{3} ln (4 - 3 x)

Solution steps

ln (14) - \frac{2}{3} ln (3 x) - \frac{4}{3} ln (4 - 3 x)

Apply log rule:

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

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

= ln (14) - ln ((3 x)^{\frac{2}{3}}) - \frac{4}{3} ln (- 3 x + 4)

Apply log rule:

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

ln (14) - ln ((3 x)^{\frac{2}{3}}) = ln (\frac{14}{( 3 x ) ^{\frac{2}{3}}})

= ln (\frac{14}{( 3 x ) ^{\frac{2}{3}}}) - \frac{4}{3} ln (- 3 x + 4)

Simplify

Apply log rule:

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

\frac{4}{3} ln (- 3 x + 4) = ln ((- 3 x + 4)^{\frac{4}{3}})

Apply log rule:

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

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

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

ln (x - 1) - ln (2 x + 1)

3 lo g_{b} (x) + lo g_{b} (y)

182000 (ln (0.45) - ln (1.3))

ln (g (x^{2} + 2))

What is ln(14)-2/3 ln(3x)-4/3 ln(4-3x) ?
The solution to ln(14)-2/3 ln(3x)-4/3 ln(4-3x) is ln((14\sqrt[3]{3}\sqrt[3]{x})/(3x(4-3x)^{4/3)})