Question

The value of $\log 3+\frac{{\left(\log 3\right)}^3}{3}+\frac{{\left(\log 3\right)}^5}{5}.................\infty$

• A. $\frac{4}{3}$
• B. $\frac{5}{4}$
• C. $\frac{3}{4}$
• D. $\frac{4}{5}$

Answer 1

The correct option is A $\frac{4}{3}$

$\begin{array}{c}Accordingtoquestion:\\ \\ \log 3+\frac{{\left(\log 3\right)}^3}{3}+\frac{{\left(\log 3\right)}^5}{5}.................\infty [\begin{array}{c}Hyperbolicformula:\\ \sinh \left(x\right)=\frac{(e^x-e^{-x})}{2}\end{array}\\ \Rightarrow \sinh \left(log3\right)=\frac{(e^{\log 3}-e^{-\log 3})}{2}\\ \Rightarrow \frac{3-\frac{1}{3}}{2}\\ \Rightarrow \frac{8}{3}\times \frac{1}{2}=\frac{4}{3}\\ sothatthecorrectoptionisA\end{array}$