What is ln(((2x+1)^{1/3})/((3x-2)^{1/4)}) ?

The solution to ln(((2x+1)^{1/3})/((3x-2)^{1/4)}) is 1/3 ln(2x+1)-1/4 ln(3x-2)

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simplify ln(((2x+1)^{1/3})/((3x-2)^{1/4)})

simplify

ln (\frac{( 2 x + 1 ) ^{\frac{1}{3}}}{( 3 x - 2 ) ^{\frac{1}{4}}})

\frac{1}{3} ln (2 x + 1) - \frac{1}{4} ln (3 x - 2)

Solution steps

ln (\frac{( 2 x + 1 ) ^{\frac{1}{3}}}{( 3 x - 2 ) ^{\frac{1}{4}}})

Apply log rule:

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

ln (\frac{( 2 x + 1 ) ^{\frac{1}{3}}}{( 3 x - 2 ) ^{\frac{1}{4}}}) = ln ((2 x + 1)^{\frac{1}{3}}) - ln ((3 x - 2)^{\frac{1}{4}})

= ln ((2 x + 1)^{\frac{1}{3}}) - ln ((3 x - 2)^{\frac{1}{4}})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= \frac{1}{3} ln (2 x + 1) - ln ((3 x - 2)^{\frac{1}{4}})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((3 x - 2)^{\frac{1}{4}}) = \frac{1}{4} ln (3 x - 2)

= \frac{1}{3} ln (2 x + 1) - \frac{1}{4} ln (3 x - 2)

ln (\frac{9}{19})

\frac{1}{5} lo g_{7} (x) + 6 lo g_{7} (w) - lo g_{7} (z)

lo g_{\frac{1}{2}} (\frac{3 x ^{2}}{2})

lo g_{3} (x) + lo g_{3} (x + 9)

What is ln(((2x+1)^{1/3})/((3x-2)^{1/4)}) ?
The solution to ln(((2x+1)^{1/3})/((3x-2)^{1/4)}) is 1/3 ln(2x+1)-1/4 ln(3x-2)