document.write( "Question 292385: I need help solving this problem:
\n" ); document.write( "\" 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.\"
\n" ); document.write( " a. Determine the value of a and b
\n" ); document.write( "Thanks a lot! \n" ); document.write( "
Algebra.Com's Answer #211258 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
y = a + b*log(x)

\n" ); document.write( "\"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:
\n" ); document.write( "7.44 = a + b*log(1)
\n" ); document.write( "Since log(1) = 0 (for all bases since \"q%5E0+=+1\") this leaves:
\n" ); document.write( "7.44 = a + b*0
\n" ); document.write( "7.44 = a

\n" ); document.write( "\"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:
\n" ); document.write( "18.36 = 7.44 + b*log(3)
\n" ); document.write( "Now we solve for b. Subtract 7.44 from each side:
\n" ); document.write( "10.92 = b*log(3)
\n" ); document.write( "Divide both sides by log(3):
\n" ); document.write( "\"%2810.92%2Flog%28%283%29%29%29+=+b\"
\n" ); document.write( "This is an exact expression for b. If you want a decimal approximation, use your calculator to find log(3) and simplify the expression.

\n" ); document.write( "This makes your equation, with the correct, exact \"a\" and \"b\":
\n" ); document.write( "\"y+=+7.44+%2B+%2810.92%2Flog%28%283%29%29%29%2Alog%28%28x%29%29\"

\n" ); document.write( "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\":
\n" ); document.write( "\"log%28%28x%29%29%2Flog%28%283%29%29+=+log%283%2C+%28x%29%29\"
\n" ); document.write( "This make the equation:
\n" ); document.write( "\"y+=+7.44+%2B10.92log%283%2C+%28x%29%29\" \n" ); document.write( "
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