Question Number 175285 by MathsFan last updated on 26/Aug/22
$$\mathrm{simplfy} \\ $$$$\:\boldsymbol{\mathrm{sinh}}\left(\boldsymbol{\mathrm{log}}\mathrm{2}\right) \\ $$
Answered by MJS_new last updated on 26/Aug/22
$$\mathrm{sinh}\:{x}\:=\frac{\mathrm{e}^{{x}} −\mathrm{e}^{−{x}} }{\mathrm{2}} \\ $$$$\Rightarrow\:\mathrm{answer}\:\mathrm{is}\:\frac{\mathrm{3}}{\mathrm{4}} \\ $$
Commented by MathsFan last updated on 26/Aug/22
$$\mathrm{can}\:\mathrm{you}\:\mathrm{please}\:\mathrm{expand}\:\mathrm{it}\:\mathrm{furter}? \\ $$
Commented by MJS_new last updated on 26/Aug/22
$$\mathrm{e}^{\mathrm{ln}\:{x}} ={x} \\ $$$$\mathrm{there}'\mathrm{s}\:\mathrm{nothing}\:\mathrm{difficult} \\ $$
Answered by MikeH last updated on 26/Aug/22
$$\mathrm{sinh}\:\left(\mathrm{ln}\:\mathrm{2}\right)\:=\:\frac{{e}^{\mathrm{ln2}} \:−{e}^{−\mathrm{ln2}} \:\:}{\mathrm{2}}\:=\:\frac{\mathrm{2}−\frac{\mathrm{1}}{\mathrm{2}}}{\mathrm{2}}\:=\:\frac{\mathrm{3}}{\mathrm{4}} \\ $$