What is simplify-ln((x^3)/(x^4+c)) ?

The solution to simplify-ln((x^3)/(x^4+c)) is -3ln(x)+ln(x^4+c)

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simplify-ln((x^3)/(x^4+c))

simplify

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

- 3 ln (x) + ln (x^{4} + c)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (x^{3}) = 3 ln (x)

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

Distribute parentheses

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

Apply minus-plus rules

- (- a) = a, - (a) = - a

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

2 lo g_{2} (a) + 2 lo g_{2} (b) + 2 lo g_{2} (a + b)

4 lo g_{6} (a) - 7 lo g_{6} (b)

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

2 ln (2) + 2 ln (x)

2 lo g_{10} (x) - \frac{1}{2} lo g_{10} (y)

What is simplify-ln((x^3)/(x^4+c)) ?
The solution to simplify-ln((x^3)/(x^4+c)) is -3ln(x)+ln(x^4+c)