Question

4 ^ n * 2 ^ 5 * (8) ^ 3 / 2 * X * (16) ^ 4 = 8 , find the value of n.​

Answer 1

Answer:

The value of n is (- 13)

Step-by-step explanation:

I guess, the question you asked is to find the value of n if

$4 ^ n * 2 ^ 5 * \frac{8^{3} }{2} * (16) ^ 4 = 8$

To proceed with the following question, you need to know some exponential formulas.

$x^{a}.x^{b}$ = $x^{a+b}$

$(x^{a})^{b}$ = $x^{ab}$

According to the question:

⇒ $4 ^ n * 2 ^ 5 * \frac{8^{3} }{2} * (16) ^ 4 = 8$

⇒ $(2^{2})^{n}$ * $2^{5}$ * $\frac{(2^{3})^{3}}{2}$ * $(2^{4})^{4}$ = 8

⇒ $2^{2n} * 2^{5} * \frac{2^{9} }{2} * 2^{16}$ = 8

⇒ $2^{2n} * 2^{5} * 2^{8} * 2^{16}$ = 8

⇒ $2^{2n + 5 + 8 + 16}$ = 8

⇒ $2^{2n + 29}$ = 8

⇒ $2^{2n + 29}$ = $2^{3}$

since the bases are same,

⇒ 2n + 29 = 3

⇒ 2n = 3 - 29

⇒ 2n = (- 26)

⇒ n = $\frac{(-26)}{2}$

⇒ n = (- 13)

∴ The value of n is (- 13)