Question

find the value of n.

8 × 2^3n = 2^12

6th grade math help me ​

Answer 1

8*2^3n=2^12
8=2^3
2^3*2^3n=2^12
2^3+3n=2^12
3+3n=12
3n=12-3
3n=9
n=9/3
n=3

Answer 2

Question :-

find the value of n.

8 × 2^3n = 2^12

Answer :-

n = 3

Solution :-

$\sf\ given \:: \: 8 \times 2 ^{3n}$

$\sf\rightarrow 8 \times 2 ^{3n} \: = {2}^{12}$

$\sf\rightarrow {2}^{3n} = {2}^{12} \: \: (8 = {2}^{3} )$

$\sf\rightarrow {2}^{3n + 3} = {2}^{12} \: \: \: ( {a}^{m} \times {a}^{n} = {a}^{m + n} )$

Equating powers since bases are same.

$\sf\rightarrow 3n \: + 3 = 12$

$\sf\rightarrow 3n \: + 3 - 3 = 12 - 3$

$\sf\rightarrow 3n = 9$

Divide both sides by 3.

$\sf\rightarrow n = 3$

Thus the value of n is 3 .