What is ln(x)-ln(sin(y/x)) ?

The solution to ln(x)-ln(sin(y/x)) is ln(xcsc(y/x))

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simplify ln(x)-ln(sin(y/x))

simplify

ln (x) - ln (sin (\frac{y}{x}))

ln (x csc (\frac{y}{x}))

Solution steps

ln (x) - ln (sin (\frac{y}{x}))

Apply log rule:

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

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

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

Use the basic trigonometric identity:

\frac{1}{sin ( x )} = csc (x)

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

- lo g_{10} (1.16 \cdot 1 0^{- 3})

- \frac{1}{3} ln (\frac{7}{4})

lo g_{e} (\frac{1}{2}) + 1

4 lo g_{2} (a) + 6 lo g_{2} (b)

ln (\frac{1}{c})

What is ln(x)-ln(sin(y/x)) ?
The solution to ln(x)-ln(sin(y/x)) is ln(xcsc(y/x))