document.write( "Question 376640: Any help would be greatly appreciated on this equation: log(x+84)-log(x+9)=log(x) \n" ); document.write( "

Algebra.Com's Answer #267959 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

You can put this solution on YOUR website!
log(x+84)- log(x+9) = log(x)
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\n" ); document.write( "Combine the 1st two logs, subtracting means divide
\n" ); document.write( " $\"log%28%28x%2B84%29%2F%28x%2B9%29%29\"$ = log(x)
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\n" ); document.write( "therefore
\n" ); document.write( " $\"%28%28x%2B84%29%2F%28x%2B9%29%29\"$ = x
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\n" ); document.write( "x + 84 = x(x+9)
\n" ); document.write( "x + 84 = x^2 + 9x
\n" ); document.write( "0 = x^2 + 9x - x - 84
\n" ); document.write( "A quadratic equation
\n" ); document.write( "x^2 + 8x - 84 = 0
\n" ); document.write( "Factors to
\n" ); document.write( "(x+14)(x-6) = 0
\n" ); document.write( "Two solutions
\n" ); document.write( "x = -14*
\n" ); document.write( "and
\n" ); document.write( "x = 6
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\n" ); document.write( "Checking solutions in original problem' only x = 6 can be a solution
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\n" ); document.write( "log(6+84)- log(6+9) = log(6)
\n" ); document.write( "log(90)- log(15) = log(6)
\n" ); document.write( "1.954 - 1.176 = .778
\n" ); document.write( ".778 = .778
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\n" ); document.write( ":
\n" ); document.write( "* the solution x=-14 would put a negative value in log(x+9) \n" ); document.write( "

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