SOLUTION: I need help solving this problem: " Public service utilities uses the equation y = a + b log x to determine the cost of electricity, where y represents the cost and x represents t

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Question 292385: I need help solving this problem:
" Public service utilities uses the equation y = a + b log x to determine the cost of electricity, where y represents the cost and x represents the time in hours. The first hour of use costs $7.44. Three hours costs $18.36."
a. Determine the value of a and b
Thanks a lot!
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
y = a + b*log(x)

"The first hour of use costs $7.44" This translates to y = 7.44 when x = 1. Putting these values into the equation we get:
7.44 = a + b*log(1)
Since log(1) = 0 (for all bases since q%5E0+=+1) this leaves:
7.44 = a + b*0
7.44 = a

"Three hours costs $18.36". This translates to y = 18.36 when x = 3. And we now know that a = 7.44. Putting these into the equation we get:
18.36 = 7.44 + b*log(3)
Now we solve for b. Subtract 7.44 from each side:
10.92 = b*log(3)
Divide both sides by log(3):
%2810.92%2Flog%28%283%29%29%29+=+b
This is an exact expression for b. If you want a decimal approximation, use your calculator to find log(3) and simplify the expression.

This makes your equation, with the correct, exact "a" and "b":
y+=+7.44+%2B+%2810.92%2Flog%28%283%29%29%29%2Alog%28%28x%29%29

If you want to get really clever you can use the fact that log%28%28x%29%29%2Flog%28%283%29%29 fits the pattern for the base conversion formula. In other "words":
log%28%28x%29%29%2Flog%28%283%29%29+=+log%283%2C+%28x%29%29
This make the equation:
y+=+7.44+%2B10.92log%283%2C+%28x%29%29