What is ln(((3x+2)^5)/(7-x^4)) ?

The solution to ln(((3x+2)^5)/(7-x^4)) is 5ln(3x+2)-ln(7-x^4)

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simplify ln(((3x+2)^5)/(7-x^4))

simplify

ln (\frac{( 3 x + 2 ) ^{5}}{7 - x ^{4}})

5 ln (3 x + 2) - ln (7 - x^{4})

Solution steps

ln (\frac{( 3 x + 2 ) ^{5}}{7 - x ^{4}})

Apply log rule:

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

ln (\frac{( 3 x + 2 ) ^{5}}{7 - x ^{4}}) = ln ((3 x + 2)^{5}) - ln (7 - x^{4})

= ln ((3 x + 2)^{5}) - ln (- x^{4} + 7)

Apply log rule:

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

ln ((3 x + 2)^{5}) = 5 ln (3 x + 2)

= 5 ln (3 x + 2) - ln (7 - x^{4})

- \frac{1}{5} ln (y + 3) + \frac{1}{5} ln (y - 2)

\frac{1}{2} ln (\frac{y}{z})

ln (e^{y} (y - 1))

lo g_{10} (\frac{z}{x ^{5}})

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

What is ln(((3x+2)^5)/(7-x^4)) ?
The solution to ln(((3x+2)^5)/(7-x^4)) is 5ln(3x+2)-ln(7-x^4)