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

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

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simplify ln(x)-ln(sin(x))

simplify

ln (x) - ln (sin (x))

ln (x csc (x))

Solution steps

ln (x) - ln (sin (x))

Apply log rule:

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

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

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

Rewrite using trig identities

= ln (x csc (x))

ln (8 x^{3}) - ln (4 x)

\frac{( ln ( \frac{1}{x + h} + 1 ) - ln ( \frac{1}{x} + 1 ) )}{h}

ln (\frac{413.15}{293.15})

- \frac{ln ( 18 )}{3 ln ( 2 ) - ln ( 3 )}

\frac{( ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣ )}{2}