What is ln(cos(x))-ln(cos(y)) ?

The solution to ln(cos(x))-ln(cos(y)) is ln(cos(x)sec(y))

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simplify ln(cos(x))-ln(cos(y))

simplify

ln (cos (x)) - ln (cos (y))

ln (cos (x) sec (y))

Solution steps

ln (cos (x)) - ln (cos (y))

Apply log rule:

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

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

= ln (\frac{cos ( x )}{cos ( y )})

Use the basic trigonometric identity:

\frac{1}{cos ( x )} = sec (x)

= ln (cos (x) sec (y))

3 lo g_{5} (u) + 4 lo g_{5} (v)

ln (\frac{0.0521}{0.101})

7 lo g_{a} (z) - \frac{1}{5} lo g_{a} (y) + 5 lo g_{a} (x)

ln (2 π \frac{L}{g})

ln (e^{- n x} x^{a} b)

What is ln(cos(x))-ln(cos(y)) ?
The solution to ln(cos(x))-ln(cos(y)) is ln(cos(x)sec(y))