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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

3 ln (x) + \frac{1}{2} ln (y) - 8

ln (\frac{200}{335}) \cdot 15

- lo g_{10} (3.3 x 1 0^{- 5})

5 lo g_{10} (x) - lo g_{10}^{2} (x)

lo g_{2} (32767) - lo g_{2} (8.3)

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