What is simplify-ln(8/(cos(x))) ?

The solution to simplify-ln(8/(cos(x))) is -3ln(2)+ln(cos(x))

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simplify-ln(8/(cos(x)))

simplify

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

- 3 ln (2) + ln (cos (x))

Solution steps

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

Apply log rule:

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

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

= - (- ln (cos (x)) + ln (8))

ln (8) = 3 ln (2)

= - (- ln (cos (x)) + 3 ln (2))

Distribute parentheses

= - (3 ln (2)) - (- ln (cos (x)))

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - 3 ln (2) + ln (cos (x))

\frac{5}{2} ln (150)

lo g_{3} (5 x^{3})

- \frac{ln ( 5 )}{2 ln ( 3 ) - ln ( 5 )}

ln (y) ln ((ln (x))^{c o s (x)})

ln (\frac{3}{3})

What is simplify-ln(8/(cos(x))) ?
The solution to simplify-ln(8/(cos(x))) is -3ln(2)+ln(cos(x))