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Solve the following logarithmic equation. Check all solutions.
\n" ); document.write( "log(x)+log(x+21)=2\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "log(x) + log(x + 21) = 2
\n" ); document.write( "logarithmic rule: logb(m) + logb(n) = logb(mn)
\n" ); document.write( "log(x(x + 21)) = 2
\n" ); document.write( "log when no base is noted is assumed to be base 10
\n" ); document.write( "logarithmic rule: if logb(y) = x then b^x = y
\n" ); document.write( "10^2 = x(x + 21)
\n" ); document.write( "100 = x^2 + 21x
\n" ); document.write( "0 = x^2 + 21x - 100
\n" ); document.write( "0 = (x + 25)(x - 4)
\n" ); document.write( "by FOIL this is x^2 - 4x + 25x - 100 or x^2 + 21x - 100
\n" ); document.write( "x = -25 or x = 4
\n" ); document.write( "can not take log of a negative number
\n" ); document.write( "10 to the something can not equal -25
\n" ); document.write( "only solution is x = 4
\n" ); document.write( "check: log(4) + log(4 + 21) = 2 = log(4) + log(25)
\n" ); document.write( "log(4) + log(25) = log(100) = 2
\n" ); document.write( "10^2 = 100, yes
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