SOLUTION: Use logarithms to solve the equation. (Round the answer to four decimal places.) 8(1.044x + 1) = 14 find x

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Use logarithms to solve the equation. (Round the answer to four decimal places.) 8(1.044x + 1) = 14 find x       Log On


   

Question 216482: Use logarithms to solve the equation. (Round the answer to four decimal places.)
8(1.044x + 1) = 14
find x
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
8%5E%281.044x+%2B+1%29+=+14

take natural logs of both sides

ln%288%5E%281.044x+%2B+1%29%29+=+ln%2814%29

Bring the exponent in front of the natural log:

%281.044x+%2B+1%29ln%288%29+=+ln%2814%29

Divide both sides by ln%288%29

%28%281.044x+%2B+1%29ln%288%29%29%2Fln%288%29+=+ln%2814%29%2Fln%288%29

%28%281.044x+%2B+1%29cross%28ln%288%29%29%29%2Fcross%28ln%288%29%29+=+ln%2814%29%2Fln%288%29

1.044x+%2B+1+=+ln%2814%29%2Fln%288%29

1.044x+=+ln%2814%29%2Fln%288%29-1

Divide both sidesa by 1.044

%281.044x%29%2F1.044+=+%28ln%2814%29%2Fln%288%29-1%29%2F1.044

%28cross%281.044%29x%29%2Fcross%281.044%29+=+%28ln%2814%29%2Fln%288%29-1%29%2F1.044

x+=+%28ln%2814%29%2Fln%288%29-1%29%2F1.044

From calculator:

x+=+0.2577761565

Rounded to four decimal places:

x=0.2578

Edwin