SOLUTION: Hello can anyone help with the following: Given x=P/Q*(1 + lnr) evaluate r when x = 0.34 P=1.08 and Q = 1.84 Many thanks.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Hello can anyone help with the following: Given x=P/Q*(1 + lnr) evaluate r when x = 0.34 P=1.08 and Q = 1.84 Many thanks.      Log On


   

Question 22376: Hello can anyone help with the following:
Given x=P/Q*(1 + lnr)
evaluate r when x = 0.34 P=1.08 and Q = 1.84
Many thanks.
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
x=P%2FQ%2A%281+%2B+lnr%29
0.34=%281.08%2F1.84%29%2A%281+%2B+ln+r+%29+

Multiply both sides by the reciprocal of 1.08%2F1.84 which is 1.84%2F1.08
0.34=%281.08%2F1.84%29%2A%281+%2B+ln+r+%29+
+%281.84%2F1.08%29%2A0.34=%281.84%2F1.08%29%2A%281.08%2F1.84%29%2A%281+%2B+ln+r+%29+
+%281.84%2F1.08%29%2A0.34=%281+%2B+ln+r+%29+

Subtract 1 from each side:
+%281.84%2F1.08%29%2A0.34-1+=+ln+r+%29+

Raise both sides as a power of e, using the famous formula e%5E%28ln+x%29=+x
+e%5E%28%281.84%2F1.08%29%2A0.34-1%29+=+e%5E%28ln+r%29+=+r+

The calculation is approximately: 0.6565602987, rounding it off to 0.66.

Forthermore, I was able to check this answer by storing the calculator value of substituting this value and the other values given in the problem in order to calculate the right side. Using the calculator value of r, you get .34, which is the value of x on the left side of the equation! It DOES check!


R^2 at SCC