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

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

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

simplify

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

ln (y sec (x))

Solution steps

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

Apply log rule:

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

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

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

Use the basic trigonometric identity:

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

= ln (y sec (x))

ln (θ (1 - θ)^{y})

- lo g_{10} (2.24 x 1 0^{- 3})

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

lo g_{10} (x^{2} - 17 x + 72) - lo g_{10} (x - 9)

ln (\frac{x ^{2} y}{3})