Q69. - Algebra 2

Question

If $4^{x+2}=48$, then $4^x=$.

$\left(A\right)3\left(B\right)6.4\left(C\right)6.9\left(D\right)12\left(E\right)24$

Step-by-Step Solution

Answer

The value of $4^x=3$ is obtained. So, option (A) is correct. 

Step 1. Write down the given equation.

The given equation is $4^{x+2}=48$.

Step 2. Simplify the equation.

The given equation $4^{x+2}=48$ is solved as:

$\begin{array}{l}{4}^{x+2}=\mathrm{48....}\left(\text{Given}\right)\\ {\left(4\right)}^x{\left(4\right)}^2=48\\ \left(16\right){\left(4\right)}^x=48\\ 4^x=3\end{array}$

Step 3. Conclusion.

Since, $4^x=3$ is obtained. So, option (A) is correct.