Question

The value of $x$, when ${\left(2\right)}^{x+4}·{\left(3\right)}^{x+1}=288$ is

• A. 1
• B. $-1$
• C. 0
• D. None

Answer 1

The correct option is A

1

Finding the value of $x:$

${\left(2\right)}^{x+4}·{\left(3\right)}^{x+1}=288$

$\Rightarrow (2^x·2^4)·(3^x·3^1)=288\left[\because a^{m+n}=a^m·a^n\right]$

$\Rightarrow {(2·3)}^x·(2^4·3^1)=288\left[\because a^m·b^m={\left(ab\right)}^m\right]$

$$\begin{gathered} \Rightarrow 6^x·(16\times 3)=288 \\ \Rightarrow 6^x·48=288 \\ \Rightarrow 6^x=\frac{288}{48} \\ \Rightarrow 6^x=6^1 \end{gathered}$$

We can observe that the bases are the same, therefore equating the powers we get,

$x=1$

Hence, option A is correct.