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You can put this solution on YOUR website!
your equation is:
\n" ); document.write( "ln(3x+5) + ln(3x-5) = 6 + ln(4)
\n" ); document.write( "subtract ln(4) from both sides of the equation to get:
\n" ); document.write( "ln(3x+5) + ln(3x-5) - ln(4) = 6
\n" ); document.write( "since ln(a) + ln(b) = ln(a*b), this equation becomes:
\n" ); document.write( "ln((3x+5)*(3x-5)) - ln(4) = 6
\n" ); document.write( "since ln(a) - ln(b) = ln(a/b), this equation becomes:
\n" ); document.write( "ln(((3x+5)*(3x-5))/4) = 6
\n" ); document.write( "since ln(a) = b if and only if e^5 = a, then you get:
\n" ); document.write( "e^6 = ((3x+5)*(3x-5))/4
\n" ); document.write( "multiply both sides of this equation by 4 to get:
\n" ); document.write( "4e^6 = (3x+5) * (3x-5)
\n" ); document.write( "since (3x+5) * (3x-5) = 9x^2 - 25, this equaton becomes:
\n" ); document.write( "4e^6 = 9x^2 - 25
\n" ); document.write( "add 25 to both sides of this equation to get:
\n" ); document.write( "9x^2 = 4e^6 + 25
\n" ); document.write( "divide both sides of this equation by 9 to get:
\n" ); document.write( "x^2 = (4e^6 + 25)/9
\n" ); document.write( "take the square root of both sides of this equation to get:
\n" ); document.write( "x = +/- sqrt((4e^6 + 25)/9)
\n" ); document.write( "that's your answer.
\n" ); document.write( "you can use your calculator to solve for the value of x.
\n" ); document.write( "you should get:
\n" ); document.write( "x = +/- 13.49368237
\n" ); document.write( "you can then substitute for x in your original equation and the equation should hold true.
\n" ); document.write( "i've done it and it does so i'm convinced.
\n" ); document.write( "actually, only x = + 13.49368237 works.
\n" ); document.write( "x = - 13.49368237 doesn't because then you are taking natural log of a negative number which is invalid.\r
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