What is ln(1/(sqrt(cos(2x)))) ?

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

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simplify ln(1/(sqrt(cos(2x))))

simplify

ln (\frac{1}{cos ( 2 x )})

- ln (cos (2 x))

Solution steps

ln (\frac{1}{cos ( 2 x )})

Apply log rule:

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

ln (\frac{1}{cos ( 2 x )}) = ln (1) - ln (cos (2 x))

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

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (cos (2 x))

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

= - ln (cos (2 x))

- ln (\frac{31}{9})

(ln (52) - ln (65)) (\frac{1}{3})

4 (ln (x) - 2 ln (2))

lo g_{2} (5) \cdot \frac{7}{8}

- lo g_{10} (6.4 \cdot 1 0^{- 8})

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