Question

If $3^x\times {27}^x=9^{x+4}$ then what is $x$ equal to?

• A. $4$
• B. $5$
• C. $6$
• D. $7$

Answer 1

The correct option is A

$4$

Explanation for correct option

Given $3^x\times {27}^x=9^{x+4}$

$\begin{array}{rcl}\therefore 3^x\times {27}^x& =& 9^{x+4}\\ & \Rightarrow & 3^x\times {\left(3^3\right)}^x={\left(3\right)}^{2\left(x+4\right)}\\ {\Rightarrow \left(3\right)}^{4x}& =& {\left(3\right)}^{2x+8}\\ & \Rightarrow & 4x=2x+8\\ & \Rightarrow & 2x=8\\ & \Rightarrow & x=4\end{array}$

Hence option (A) is correct