Question

If $\tanh (x)=\frac{1}{3}$ then $\tanh (3x)$ is

• A. $\frac{8}{9}$
• B. $\frac{7}{9}$
• C. $1$
• D. $\frac{2}{3}$

Answer 1

Answer: (B)

$\tanh (x)=\frac{1}{3},\tanh (3x)=?$
$\Rightarrow \frac{e^x-e^{-x}}{e^x+e^{-x}}=\frac{1}{3}$
$\Rightarrow 2e^x=4e^{-x}$
$\Rightarrow \left(e^{2x}=2\right)$ and
$\tanh (3x)=\frac{e^{3x}-e^{-3x}}{e^{3x}+e^{-3x}}=\frac{{\left(e^{2x}\right)}^3-1}{{\left(e^{2x}\right)}^3+1}$
$=\frac{8-1}{8+1}=\frac{7}{9}$