What is ln((xsqrt(x^3-1))/(x^5+9)) ?

The solution to ln((xsqrt(x^3-1))/(x^5+9)) is ln(x)+ln(sqrt(x^3-1))-ln(x^5+9)

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simplify ln((xsqrt(x^3-1))/(x^5+9))

simplify

ln (\frac{x x ^{3} - 1}{x ^{5} + 9})

ln (x) + ln (x^{3} - 1) - ln (x^{5} + 9)

Solution steps

ln (\frac{x x ^{3} - 1}{x ^{5} + 9})

Apply log rule:

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

ln (\frac{x x ^{3} - 1}{x ^{5} + 9}) = ln (x x^{3} - 1) - ln (x^{5} + 9)

= ln (x x^{3} - 1) - ln (x^{5} + 9)

Apply log rule:

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

ln (x x^{3} - 1) = ln (x) + ln (x^{3} - 1)

= ln (x) + ln (x^{3} - 1) - ln (x^{5} + 9)

\frac{1}{2} lo g_{c} (x) + 4 lo g_{c} (y) - 5 lo g_{c} (x)

lo g_{3} (\frac{2 x - 1}{5 x + 2})

lo g_{10} (\frac{6 w ^{5}}{x})

ln (\frac{729}{10000})

lo g_{2} (x^{2}) - 5 \cdot lo g_{2} (x) + 4

What is ln((xsqrt(x^3-1))/(x^5+9)) ?
The solution to ln((xsqrt(x^3-1))/(x^5+9)) is ln(x)+ln(sqrt(x^3-1))-ln(x^5+9)