What is ln((x^2)/(esqrt(x)cos(x))) ?

The solution to ln((x^2)/(esqrt(x)cos(x))) is 2ln(x)-1-ln(sqrt(x))-ln(cos(x))

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simplify ln((x^2)/(esqrt(x)cos(x)))

simplify

ln (\frac{x ^{2}}{e x cos ( x )})

2 ln (x) - 1 - ln (x) - ln (cos (x))

Solution steps

ln (\frac{x ^{2}}{e x cos ( x )})

Apply log rule:

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

ln (\frac{x ^{2}}{e x cos ( x )}) = ln (x^{2}) - ln (e x cos (x))

= ln (x^{2}) - ln (e x cos (x))

Apply log rule:

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

ln (x^{2}) = 2 ln (x)

= 2 ln (x) - ln (e x cos (x))

Apply log rule:

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

ln (e x cos (x)) = ln (e) + ln (x) + ln (cos (x))

= 2 ln (x) - (ln (x) + ln (cos (x)) + ln (e))

Apply log rule:

lo g_{a} (a) = 1

= 2 ln (x) - (ln (x) + ln (cos (x)) + 1)

- (1 + ln (x) + ln (cos (x))) : - 1 - ln (x) - ln (cos (x))

= 2 ln (x) - 1 - ln (x) - ln (cos (x))

ln (\frac{496200}{40100})

ln (x^{3} e^{2})

2 ln (x) - ln (x + 2)

ln (e) + ln (\frac{1}{10})

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

What is ln((x^2)/(esqrt(x)cos(x))) ?
The solution to ln((x^2)/(esqrt(x)cos(x))) is 2ln(x)-1-ln(sqrt(x))-ln(cos(x))