document.write( "Question 41576: Solve the following equations:\r
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Algebra.Com's Answer #26855 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
Solve the following equations:\r\n" );
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document.write( "a) 5^(2x+1) = 48     b) log6(x+41)-log4(x+1)=2\r\n" );
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document.write( "   52x+1 = 48\r\n" );
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document.write( "Take logs of both sides\r\n" );
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document.write( "  log(52x+1) = log(48)\r\n" );
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document.write( "Use the rule:   log(AB) = B·log(A) on the left side\r\n" );
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document.write( " (2x+1)log(5) = log(48)\r\n" );
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document.write( "Divide both sides by log(5)\r\n" );
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document.write( " (2x+1)log(5)    log(48)\r\n" );
document.write( " ———————————— =  —————————\r\n" );
document.write( "    log(5)        log(5)\r\n" );
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document.write( "         1 \r\n" );
document.write( " (2x+1)log(5)    log(48)\r\n" );
document.write( " ———————————— = —————————\r\n" );
document.write( "    log(5)        log(5)\r\n" );
document.write( "      1\r\n" );
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document.write( "                 log(48)\r\n" );
document.write( "       2x + 1 = —————————\r\n" );
document.write( "                  log(5) \r\n" );
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document.write( "                 log(48)\r\n" );
document.write( "           2x = ————————— - 1\r\n" );
document.write( "                  log(5)\r\n" );
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document.write( "                 log(48)     log(5)\r\n" );
document.write( "           2x = ————————— - —————————\r\n" );
document.write( "                  log(5)     log(5)\r\n" );
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document.write( "                 log(48) - log(5)\r\n" );
document.write( "           2x = ——————————————————\r\n" );
document.write( "                      log(5) \r\n" );
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document.write( "Divide both sides by 2:\r\n" );
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document.write( "                 log(48) - log(5)\r\n" );
document.write( "            x = ——————————————————\r\n" );
document.write( "                    2·log(5) \r\n" );
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document.write( "                 1.681241237 - 0.6989700043\r\n" );
document.write( "            x = ————————————————————————————\r\n" );
document.write( "                    2·(0.6989700043)\r\n" );
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document.write( "                 0.982271233\r\n" );
document.write( "            x = —————————————\r\n" );
document.write( "                 1.397940009\r\n" );
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document.write( "            x = .7026562134\r\n" );
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document.write( "===============================================\r\n" );
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document.write( " b) \r\n" );
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document.write( "       log6(x+41) - log4(x+1) = 2\r\n" );
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document.write( "Use rule:   \r\n" );
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document.write( "log(A) - log(B) = log(A/B) on left side\r\n" );
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document.write( "                    æ6(x+41)ö	\r\n" );
document.write( "                log ç———————÷ = 2\r\n" );
document.write( "                    è 4(x+1)ø \r\n" );
document.write( "                       \r\n" );
document.write( "Use the rule: log(A) = B is equivalent to\r\n" );
document.write( "the equation A = 10B  \r\n" );
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document.write( "                      6(x+41)\r\n" );
document.write( "                     ———————— = 102\r\n" );
document.write( "                       4(x+1)  \r\n" );
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document.write( "                      3\r\n" );
document.write( "                      6(x+41)\r\n" );
document.write( "                     ———————— = 102\r\n" );
document.write( "                       4(x+1)   \r\n" );
document.write( "                       2\r\n" );
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document.write( "                      3(x+41)\r\n" );
document.write( "                     ———————— = 100\r\n" );
document.write( "                       2(x+1)\r\n" );
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document.write( "Multiply both sides by 2(x+1)\r\n" );
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document.write( "                      3(x+41) = 100·2(x+1)\r\n" );
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document.write( "                      3(x+41) = 200(x+1)\r\n" );
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document.write( "                     3x + 123 = 200x + 200            \r\n" );
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document.write( "                        -197x = 77\r\n" );
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document.write( "                            x = -77/197\r\n" );
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document.write( "Edwin McCravy\r\n" );
document.write( "AnlytcPhil@aol.com
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