What is ln((5x^4)/(cos(x))) ?

The solution to ln((5x^4)/(cos(x))) is ln(5)+4ln(x)-ln(cos(x))

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simplify ln((5x^4)/(cos(x)))

simplify

ln (\frac{5 x ^{4}}{cos ( x )})

ln (5) + 4 ln (x) - ln (cos (x))

Solution steps

ln (\frac{5 x ^{4}}{cos ( x )})

Apply log rule:

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

ln (\frac{5 x ^{4}}{cos ( x )}) = ln (5 x^{4}) - ln (cos (x))

= ln (5 x^{4}) - ln (cos (x))

Apply log rule:

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

ln (5 x^{4}) = ln (5) + ln (x^{4})

= ln (5) + ln (x^{4}) - ln (cos (x))

Apply log rule:

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

ln (x^{4}) = 4 ln (x)

= ln (5) + 4 ln (x) - ln (cos (x))

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ln (72) - 2 ln (3)

What is ln((5x^4)/(cos(x))) ?
The solution to ln((5x^4)/(cos(x))) is ln(5)+4ln(x)-ln(cos(x))