What is ln((x^{17}sqrt(x-1))/(3x-10)) ?

The solution to ln((x^{17}sqrt(x-1))/(3x-10)) is 17ln(x)+ln(sqrt(x-1))-ln(3x-10)

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simplify ln((x^{17}sqrt(x-1))/(3x-10))

simplify

ln (\frac{x ^{17} x - 1}{3 x - 10})

17 ln (x) + ln (x - 1) - ln (3 x - 10)

Solution steps

ln (\frac{x ^{17} x - 1}{3 x - 10})

Apply log rule:

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

ln (\frac{x ^{17} x - 1}{3 x - 10}) = ln (x^{17} x - 1) - ln (3 x - 10)

= ln (x^{17} x - 1) - ln (3 x - 10)

Apply log rule:

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

ln (x^{17} x - 1) = ln (x^{17}) + ln (x - 1)

= ln (x^{17}) + ln (x - 1) - ln (3 x - 10)

Apply log rule:

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

ln (x^{17}) = 17 ln (x)

= 17 ln (x) + ln (x - 1) - ln (3 x - 10)

lo g_{b} (\frac{25}{9})

2 lo g_{3} (k) - 3 - lo g_{3} (x)

ln (\frac{x ^{2} - 0.25}{2})

\frac{1}{540} ln (\frac{100}{32.5})

ln (\frac{x ^{8} p ^{5} q}{e ^{5}})

What is ln((x^{17}sqrt(x-1))/(3x-10)) ?
The solution to ln((x^{17}sqrt(x-1))/(3x-10)) is 17ln(x)+ln(sqrt(x-1))-ln(3x-10)