If the 7th term in the binomial expansion of ([3]84+√3^ x)^9, x0, is equal to 729, then x…

Question

If the 7th term in the binomial expansion of $\left(\sqrt[3]{\dfrac{8}{4}}+\sqrt3{}^{\ln x}\right)^9$, $x>0$, is equal to 729, then $x$ can be:

Accepted Answer

$T_7=T_{6+1}=\binom96\left(	ext{base}_1ight)^3\left(\sqrt3^{\ln x}ight)^6=729$. Following the source's simplification: $3^6=\ldots	imes(\ln x)^6$, giving $(\ln x)^6=(\ln e)^6\Rightarrow x=e$.

$x=e$

Solutions · 1