What is ln((x^{16}sqrt(x-1))/(3x-12)) ?

The solution to ln((x^{16}sqrt(x-1))/(3x-12)) is 16ln(x)+ln(sqrt(x-1))-ln(3x-12)

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simplify ln((x^{16}sqrt(x-1))/(3x-12))

simplify

ln (\frac{x ^{16} x - 1}{3 x - 12})

16 ln (x) + ln (x - 1) - ln (3 x - 12)

Solution steps

ln (\frac{x ^{16} x - 1}{3 x - 12})

Apply log rule:

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

ln (\frac{x ^{16} x - 1}{3 x - 12}) = ln (x^{16} x - 1) - ln (3 x - 12)

= ln (x^{16} x - 1) - ln (3 x - 12)

Apply log rule:

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

ln (x^{16} x - 1) = ln (x^{16}) + ln (x - 1)

= ln (x^{16}) + ln (x - 1) - ln (3 x - 12)

Apply log rule:

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

ln (x^{16}) = 16 ln (x)

= 16 ln (x) + ln (x - 1) - ln (3 x - 12)

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ln (2 e^{\frac{A}{e}})

2 \cdot ln (7) - 2 \cdot ln (6) + 2 \cdot ln (8) - 2 \cdot ln (7)

lo g_{10} (\frac{2 ( - 5 + 2 5 )}{- 5 + 5})

ln (\frac{x ^{5}}{x ^{2} - 36})

What is ln((x^{16}sqrt(x-1))/(3x-12)) ?
The solution to ln((x^{16}sqrt(x-1))/(3x-12)) is 16ln(x)+ln(sqrt(x-1))-ln(3x-12)