Question

The 10th term in the expansion of $5^x$ is

• A. $\frac{x^{10}}{10!}$
• B. $\frac{x^9}{9!}$
• C. $\frac{x^9}{9!}(lo{g}_{e}5{)}^9$
• D. $\frac{x^{10}}{10!}(lo{g}_{e}5{)}^{10}$

Answer 1

The correct option is C $\frac{x^9}{9!}(lo{g}_{e}5{)}^9$

$5^x=e^{x\log 5}={\sum }_{n=0}^{\infty }\frac{(x\log 5{)}^n}{n!}$

So ${10}^{th}$ term $=$ $\frac{(x\log 5{)}^9}{9!}$ when $n=9$