document.write( "Question 92471: If logb 2=x and logb 3=y, evaluate the following in terms of x and y:
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Algebra.Com's Answer #67320 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "If logb2 = x and logb3 = y, evaluate the following in terms of x and y:\r\n" );
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document.write( "You need these three rules:\r\n" );
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document.write( "1.     logb(ac) = logba + logbc\r\n" );
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document.write( "2.     logb\"a%2Fc\" = logba - logbc\r\n" );
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document.write( "3.     logb\"a%5Ec\" = c·logba\r\n" );
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document.write( "(a) logb216=\r\n" );
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document.write( "Break 216 down to primes:\r\n" );
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document.write( "216 = \"2%2A108\" = \"2%2A2%2A54\" = \"2%2A2%2A2%2A27\" = \"2%2A2%2A2%2A3%2A9\" = \"2%2A2%2A2%2A3%2A3%2A3\" = \"2%5E3%2A3%5E3\"\r\n" );
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document.write( "logb216 = logb\"2%5E3%2A3%5E3\" \r\n" );
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document.write( "= logb\"2%5E3\" + logb\"3%5E3\"     (by rule 1.)\r\n" );
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document.write( "= 3·logb2 + 3·logb3                 (by rule 3.)\r\n" );
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document.write( "= 3·x + 3·y                         (by substitution.) \r\n" );
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document.write( "= 3(x + y) \r\n" );
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document.write( "=============================================\r\n" );
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document.write( "(b) logb162=\r\n" );
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document.write( "Break 162 down to primes:\r\n" );
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document.write( "162 = \"2%2A81\" = \"2%2A9%2A9\" = \"2%2A3%2A3%2A3%2A3\" = \"2%2A3%5E4\"\r\n" );
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document.write( "logb162 = logb\"2%2A3%5E4\" \r\n" );
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document.write( "= logb2 + logb\"3%5E4\"     (by rule 1.)\r\n" );
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document.write( "= logb2 + 4·logb3           (by rule 3.)\r\n" );
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document.write( "= x + 4·y                   (by substitution.) \r\n" );
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document.write( "= x + 4y \r\n" );
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document.write( "=======================================\r\n" );
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document.write( "(c) logb\"2%2F9\"\r\n" );
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document.write( "Break the 9 in the denominator down into primes\r\n" );
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document.write( "9 = \"3%2A3\" = \"3%5E2\"\r\n" );
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document.write( "logb\"2%2F9\" = logb\"2%2F3%5E2\"\r\n" );
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document.write( "= logb2 - logb\"3%5E2\"\r\n" );
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document.write( "= logb2 - 2·logb3\r\n" );
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document.write( "= x - 2y\r\n" );
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document.write( "============================================\r\n" );
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document.write( "(d) \r\n" );
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document.write( " logb9\r\n" );
document.write( "———————    \r\n" );
document.write( " logb8\r\n" );
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document.write( "Break the 9 down as \"3%5E2\" and the 8 down as \"2%5E3\"\r\n" );
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document.write( " logb9     logb\"3%5E2\"\r\n" );
document.write( "——————— = —————————    \r\n" );
document.write( " logb8     logb\"2%5E3\"\r\n" );
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document.write( " 2·logb3\r\n" );
document.write( "—————————                (by rule 3.)    \r\n" );
document.write( " 3·logb2\r\n" );
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document.write( "\"%282y%29%2F%283x%29\"            (substitution)\r\n" );
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document.write( "Edwin
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