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 * 2 ^(3n)`

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

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

`\sf\rightarrow {2}^(3n + 3) = {2}^(12) \: \: \: ( {a}^(m) * {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 .