1. ## hyperbolic function problem

can anybody help me with the question below??
simplify:
sech(3log (x))

i dont have a clue how to simplify this kind of question, anybody give me hand?>>
thanx!!

2. Originally Posted by xixihaha
can anybody help me with the question below??
simplify:
sech(3log (x))

i dont have a clue how to simplify this kind of question, anybody give me hand?>>
thanx!!

Alright I fixed it (I think)

$sech(x)=\frac{2}{e^x+e^{-x}}$

note:

$e^{3log{x}}=e^{log{x^3}}=e^{\frac{lnx^3}{ln10}}=\l eft(e^{lnx^3}\right)^{\frac{1}{ln10}}=x^\frac{3}{l n10}$

evaluating the above we get..

$sech(3log(x))=\frac{2}{e^{logx^3}+e^{-logx^3}}$

simplifying with the above

$\frac{2}{e^{logx^3}+e^{-logx^3}}=\frac{2}{x^\frac{3}{ln10}+x^\frac{-3}{ln10}}=\frac{2x^\frac{3}{ln10}}{x^\frac{6}{ln10 }+1}$