document.write( "Question 130285: The current price of a litre of gasoline is $0.92 and is expected to increase at a rate of 12% every six months.The price of a litre of diesel is $0.80 and is expected to increase at a rate of 15% every 4 months. If these trends continue, after how many months will both fuels have the same price per litre? \n" ); document.write( "

Algebra.Com's Answer #95225 by scott8148(6628) $\"\"$ $\"About$

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let x=\"months until same price\"\r
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\n" ); document.write( "\n" ); document.write( "92(1.12)^(x/6)=80(1.15)^(x/4) __ dividing by 80 __ 1.15(1.12)^(x/6)=(1.15)^(x/4)\r
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\n" ); document.write( "\n" ); document.write( "taking log __ log(1.15)+(x/6)(log(1.12))=(x/4)(log(1.15))\r
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\n" ); document.write( "\n" ); document.write( "subtracting (x/6)(log(1.12))__ log(1.15)=(x/4)(log(1.15))-(x/6)(log(1.12))\r
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\n" ); document.write( "\n" ); document.write( "factoring __ log(1.15)=x[(log(1.15))/4-(log(1.12))/6]\r
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\n" ); document.write( "\n" ); document.write( "dividing by [(log(1.15))/4-(log(1.12))/6] __ (log(1.15))/[(log(1.15))/4-(log(1.12))/6]=x \n" ); document.write( "

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