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Find the value of n.

8 × 2^3n = 2^12

6th grade math help me ​

User Bing Wang
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11 votes
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
Find the value of n. 8 × 2^3n = 2^12 6th grade math help me ​-example-1
User Liam Bigelow
by
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7 votes

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 .

User Michael Beale
by
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