What is ln((x^8cos^4(x))/(sqrt(x-4))) ?

The solution to ln((x^8cos^4(x))/(sqrt(x-4))) is 8ln(x)+ln(cos^4(x))-ln(sqrt(x-4))

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simplify ln((x^8cos^4(x))/(sqrt(x-4)))

simplify

ln (\frac{x ^{8} cos ^{4} ( x )}{x - 4})

8 ln (x) + ln (cos^{4} (x)) - ln (x - 4)

Solution steps

ln (\frac{x ^{8} cos ^{4} ( x )}{x - 4})

Apply log rule:

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

ln (\frac{x ^{8} cos ^{4} ( x )}{x - 4}) = ln (x^{8} cos^{4} (x)) - ln (x - 4)

= ln (x^{8} cos^{4} (x)) - ln (x - 4)

Apply log rule:

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

ln (x^{8} cos^{4} (x)) = ln (x^{8}) + ln (cos^{4} (x))

= ln (x^{8}) + ln (cos^{4} (x)) - ln (x - 4)

Apply log rule:

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

ln (x^{8}) = 8 ln (x)

= 8 ln (x) + ln (cos^{4} (x)) - ln (x - 4)

- a (ln ∣ a - l ∣ - ln ∣ a ∣) - l

\frac{1}{2} ln (\frac{386000}{530000})

ln (\frac{50000}{20000})

e^{x - 2 y} - ln (2 x^{2} y)

\frac{1}{lo g _{10} ( 62.8 ) - lo g _{10} ( 6.28 )}

What is ln((x^8cos^4(x))/(sqrt(x-4))) ?
The solution to ln((x^8cos^4(x))/(sqrt(x-4))) is 8ln(x)+ln(cos^4(x))-ln(sqrt(x-4))