SOLUTION: Hello, can anyone assist with this: Obtain the value for v given that S = 1.59t ^ (1-3v) when S = 3.52 and t = 21.56 Thanks.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hello, can anyone assist with this: Obtain the value for v given that S = 1.59t ^ (1-3v) when S = 3.52 and t = 21.56 Thanks.      Log On


   

Question 22373: Hello, can anyone assist with this:
Obtain the value for v given that
S = 1.59t ^ (1-3v)
when S = 3.52 and t = 21.56




Thanks.
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
S+=+1.59t+%5E+%281-3v%29+
3.52+=+1.59%2A21.56+%5E+%281-3v%29+

Divide both sides by 1.59, but do NOT calculate and round off the value on the left side! This can cause serious error propagation.
3.52%2F1.59=21.56+%5E+%281-3v%29+

Next, take the ln of both sides of the equation:
ln%283.52%2F1.59%29=+ln%2821.56+%5E+%281-3v%29+%29+

Use the law of logarithms ln+M%5EN+=+N+%2Aln+M:
ln%283.52%2F1.59%29=+%281-3v%29+%2Aln%2821.56+%29+


Use the distributive property to remove the parentheses:
ln%283.52%2F1.59%29=+1%2Aln%2821.56%29+-3v+%2Aln%2821.56+%29+

Subtract ln (21.56) from both sides:
ln%283.52%2F1.59%29-+1%2Aln%2821.56%29+=+-3v+%2Aln%2821.56+%29+

Divide both sides by -3ln(21.56):

%28%28ln%283.52%2F1.59%29-+1%2Aln%2821.56%29%29%29%2F%28-3%2Aln%2821.56%29%29+=+v+

Calculate with a calculator if you have one. I got v = 0.2470673563 approximately. It probably should be rounded off to v=0.247, since the problem is only accurate to three significant digits.

You can check this by substituting all the numbers into the original equation and calculating the result to see if it really works. When I did this I found that my first attempt was WRONG!! This answer checks!!

R^2 at SCC