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

Question

Aicharya · Accepted Answer

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

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

Solution