What is ln(cosh(b))-ln(cosh(a)) ?

The solution to ln(cosh(b))-ln(cosh(a)) is ln(cosh(b)sech(a))

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simplify ln(cosh(b))-ln(cosh(a))

simplify

ln (cosh (b)) - ln (cosh (a))

ln (cosh (b) sech (a))

Solution steps

ln (cosh (b)) - ln (cosh (a))

Apply log rule:

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

ln (cosh (b)) - ln (cosh (a)) = ln (\frac{cosh ( b )}{cosh ( a )})

= ln (\frac{cosh ( b )}{cosh ( a )})

Use the Hyperbolic identity:

\frac{1}{cosh ( x )} = sech (x)

= ln (cosh (b) sech (a))

ln ((x^{3} + 2) (x^{2} + 3))

lo g_{4} (2) + 2 lo g_{4} (3)

x - ln (e^{x} cos (x))

lo g_{5} (\frac{f}{25})

ln (\frac{83}{4})

What is ln(cosh(b))-ln(cosh(a)) ?
The solution to ln(cosh(b))-ln(cosh(a)) is ln(cosh(b)sech(a))