Question

${2}^{3} \times {4}^{n} = {2}^{11}$2^3 x 4^n = 2^11Find the value of the variable.

Answer 1

Answer:

n = 4

Explanation:

To find the value of n, we will use the following properties:

$\begin{gathered} \frac{2^a}{2^b}=2^{a-b} \\ 4^n=2^{2n} \end{gathered}$

Now, we have the expression:

$2^3\cdot4^n=2^{11}$

Divide both sides by 2³, so:

$\begin{gathered} \frac{2^3\cdot4^n}{2^3}=\frac{2^{11}}{2^3} \\ 4^n=2^{11-3} \\ 4^n=2^8 \end{gathered}$

Then, we can replace 4^n by 2^(2n), so:

$2^{2n}=2^8$

Since the base on both sides is equal to 2, we can equal the exponents, so:

$2n=8$

Finally, divide both sides by 2, so:

$\begin{gathered} \frac{2n}{2}=\frac{8}{2} \\ n=4 \end{gathered}$

So, the value of n is 4.