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You can put this solution on YOUR website!
For a specified real number, twice the log of the number that is two less than the specified number will equal the log of the number that is 8 less than 3 times the specified number.
\n" ); document.write( "what could the specified number possibly be?
\n" ); document.write( ":
\n" ); document.write( "Let x = a specified number
\n" ); document.write( ":
\n" ); document.write( "Write an equation for statement, (commas help):
\n" ); document.write( "\"twice the log of the number, that is two less than the specified number, will equal the log of the number, that is 8 less than 3 times the specified number.\"
\n" ); document.write( ":
\n" ); document.write( "2*log(x-2) = log(3x-8)
\n" ); document.write( "The exponent equiv
\n" ); document.write( "log((x-2)^2) = log(3x-8)
\n" ); document.write( "therefore
\n" ); document.write( "(x-2)^2 = 3x - 8
\n" ); document.write( "FOIL the left side:
\n" ); document.write( "x^2 - 4x + 4 = 3x - 8
\n" ); document.write( "x^2 - 4x - 3x + 4 + 8 = 0
\n" ); document.write( "x^2 - 7x + 12 = 0
\n" ); document.write( "Factors to
\n" ); document.write( "(x-4)(x-3) = 0
\n" ); document.write( "Two solutions as the specified number
\n" ); document.write( "x=4
\n" ); document.write( "x=3
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check solution x=4 in the original equation
\n" ); document.write( "2*log(4-2) = log(3(4)-8)
\n" ); document.write( "2*log(2) = log(4); confirms our solution
\n" ); document.write( ":
\n" ); document.write( "You can check the x=3 solution (remember log of 1 = 0)\r
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