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You can put this solution on YOUR website!
3*log(x) + 6*log(x-2) would be equivalent to:
\n" ); document.write( "log(x^3) + log((x-2)^6) which would then be equivalent to:
\n" ); document.write( "log(x^3 * (x-2)^6)
\n" ); document.write( "the 2 properties of logarithms that are used are:
\n" ); document.write( "log(a*b) = log(a) + log(b)
\n" ); document.write( "log(a^b) = b*log(a)
\n" ); document.write( "you need to apply them in the correct order.
\n" ); document.write( "assume you started with:
\n" ); document.write( "log(x^3 * (x-2)^6)
\n" ); document.write( "you would use log(a*b) = log(a) + log(b) to get:
\n" ); document.write( "log(x^3) + log(x-2)^6)
\n" ); document.write( "you would then use log(a^b) = b*log(a) to get:
\n" ); document.write( "3*log(x) + 6*log(x-2)
\n" ); document.write( "to confirm you have the correct answer, substitute random values for x and solve using the original equation and the final equation to see if you get the same answer with each.
\n" ); document.write( "assuming x is equal to 9, solve each in turn.
\n" ); document.write( "original equation:
\n" ); document.write( "3*log(x) + 6*log(x-2) is equal to:
\n" ); document.write( "3*log(9) + 6*log(9-2) which is equal to:
\n" ); document.write( "3*log(9) + 6*log(7) which is equal to:
\n" ); document.write( "7.933315768
\n" ); document.write( "final equation:
\n" ); document.write( "log(x^3 * (x-2)^6) is equal to:
\n" ); document.write( "log(9^3 * (9-2)^6) which is equal to:
\n" ); document.write( "log(9^3 * 7^6) which is equal to:
\n" ); document.write( "log(729 * 117649) which is equal to:
\n" ); document.write( "log(85766121) which is equal to:
\n" ); document.write( "7.933315768
\n" ); document.write( "the answer are the same so you can reasonably assume that the conversion was done successfully.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "