Solve for x

[nycmathguy]

 

[MathLover1]

8(4^(6-2x))+13=41

8(4^(6-2x))=41-13

8(4^(6-2x))=28

4^(6-2x))=28/8

4^(6-2x))=7/2............take log of both sides

log((4^(6-2x))=log(7/2)

(6-2x)log(4)=log(7)-log(2)

(6-2x)=(log(7)-log(2))/log(2^2)

6-2x=(log(7)-log(2))/(2log(2))

6-(log(7)-log(2))/(2log(2))=2x

2x=13/2 - log(7)/(2 log(2))

x=(13/2 - log(7)/(2 log(2)))/2

x=13/4 - log(7)/(4log(2))

 

[nycmathguy]

8(4^(6-2x))+13=41

8(4^(6-2x))=41-13

8(4^(6-2x))=28

4^(6-2x))=28/8

4^(6-2x))=7/2............take log of both sides

log((4^(6-2x))=log(7/2)

(6-2x)log(4)=log(7)-log(2)

(6-2x)=(log(7)-log(2))/log(2^2)

6-2x=(log(7)-log(2))/(2log(2))

6-(log(7)-log(2))/(2log(2))=2x

2x=13/2 - log(7)/(2 log(2))

x=(13/2 - log(7)/(2 log(2)))/2

x=13/4 - log(7)/(4log(2))

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