document.write( "Question 552279: My teacher did not explain any of this stuff to us, so if someone could please EXPLAIN both these types of problums to me that would be awesome.
\n" ); document.write( "1) log 7 = 0.8
\n" ); document.write( " log 12 = 1.1
\n" ); document.write( " log 8= 0.9
\n" ); document.write( "Find log 1/64\r
\n" ); document.write( "\n" ); document.write( "2)log[5] 11 = 1.5
\n" ); document.write( " log[5] 6 = 1.1
\n" ); document.write( " log[5] 4 =0.9
\n" ); document.write( "Find log[5] 264 \n" ); document.write( "
Algebra.Com's Answer #360213 by AnlytcPhil(1807)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "logB(A) asks the question:\r\n" );
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document.write( "To what exponent must the base B be raised to give A?  \r\n" );
document.write( "That exponent is the answer to what logB(A) equals. \r\n" );
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document.write( "Because logarithms are exponents, and because we can \r\n" );
document.write( "add exponents of a base in order to multiply, subtract them in \r\n" );
document.write( "order to divide, and multiply them to raise a power to a power, \r\n" );
document.write( "we have these three corresponding rules for logarithms:\r\n" );
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document.write( "1.  logB(A·C) = logB(A) + logB(C)\r\n" );
document.write( "2.  logB\"%28A%2FC%29\" = logB(A) - logB(C)\r\n" );
document.write( "3.  logB(AC) = C·logB(A)\r\n" );
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document.write( "[If the base B isn't written, it's understood to be 10.]\r\n" );
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document.write( "1) log(7) = 0.8\r\n" );
document.write( "log(12) = 1.1\r\n" );
document.write( "log(8)= 0.9\r\n" );
document.write( "Find log\"%281%2F64%29\"\r\n" );
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document.write( "Use rule 2:\r\n" );
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document.write( "2.  logB\"%28A%2FC%29\" = logB(A) - logB(C)\r\n" );
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document.write( "with A=1, B=64, and the base B understood as 10\r\n" );
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document.write( "    log\"%281%2F64%29\" = log(1) - log(64)\r\n" );
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document.write( "Now we use the definition of logarithms to find log(1).\r\n" );
document.write( "We ask the question \"To what power must the base 10 be raised to get 1?\"\r\n" );
document.write( "If you remember that 100 = 1, then you know that log(1)\r\n" );
document.write( "is 0.  In fact the logarithm of 1 is always 0, regardless of the base.  \r\n" );
document.write( "So now we have\r\n" );
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document.write( "    log\"%281%2F64%29\" = 0 - log(64)\r\n" );
document.write( "or\r\n" );
document.write( "     -log(64)\r\n" );
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document.write( "We are given the values of these three logs with understood base 10: \r\n" );
document.write( " log(7) = 0.8, log(12) = 1.1, log(8)= 0.9\r\n" );
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document.write( "Now we ask:  Which of these numbers 7, 12, or 8, can we multiply\r\n" );
document.write( "together, divide, or raise to a power, to get 64?\r\n" );
document.write( "The answer: we can get 64 by squaring 8. That is, 8² = 64.\r\n" );
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document.write( "So we replace 64 by 8² and now we have:\r\n" );
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document.write( "     -log(8²)\r\n" );
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document.write( "Now we use rule 3:\r\n" );
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document.write( "3.  logB(AC) = C·logBA\r\n" );
document.write( "with A=8 and C=2\r\n" );
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document.write( "and we have:\r\n" );
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document.write( "   -log(82) = -2·log(8)\r\n" );
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document.write( "And since we are given log(8) = 0.9\r\n" );
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document.write( "   -2·log(8)\r\n" );
document.write( "   -2·(0.9)\r\n" );
document.write( "     -1.8 \r\n" );
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document.write( "That's the answer, -1.8.  Try hard to follow the above.\r\n" );
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document.write( "2)log5(11) = 1.5\r\n" );
document.write( "log5(6) = 1.1\r\n" );
document.write( "log5(4) = 0.9\r\n" );
document.write( "Find log5(264)\r\n" );
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document.write( "We are given the values of these three logs with base 5: \r\n" );
document.write( "log5(11) = 1.5, log5(6) = 1.1, log5(4) = 0.9\r\n" );
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document.write( "Now we ask:  Which of these numbers 11, 6, and 4, can we multiply\r\n" );
document.write( "together, divide, or raise to a power, to get 264?\r\n" );
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document.write( "To answer that we must see if 264 can be divided evenly by one of those.\r\n" );
document.write( "We find the 264÷11 = 24. So we write \r\n" );
document.write( "264 = = 11·24 and we write\r\n" );
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document.write( "   log5(264) = \r\n" );
document.write( "   log5(11·24)\r\n" );
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document.write( "Now we use rule 1:\r\n" );
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document.write( "1.  logB(A·C) = logB(A) + logB(C)\r\n" );
document.write( "with A=11, B=5, C=24\r\n" );
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document.write( "    log5(11·24) = log5(11) + log5(24)\r\n" );
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document.write( "We substitute the given log5(11) = 1.5, and we have:\r\n" );
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document.write( "    1.5 + log5(24)\r\n" );
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document.write( "Now we ask:  Which of these numbers 11, 6, and 4, can we multiply\r\n" );
document.write( "together, divide, or raise to a power, to get 24?  That answer is easy.\r\n" );
document.write( "24 = 6·4.  So we replace 24 by 6·4, and we have:\r\n" );
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document.write( "    1.5 + log5(6·4)\r\n" );
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document.write( "Now we use rule 1 again:\r\n" );
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document.write( "1.  logB(A·C) = logB(A) + logB(C)\r\n" );
document.write( "this time with with A=6, B=5, C=4\r\n" );
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document.write( "    1.5 + log5(6) + log5(4)\r\n" );
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document.write( "and we are give those logs, so we substitute:\r\n" );
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document.write( "    1.5 + 1.1 + 0.9\r\n" );
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document.write( "Answer: 3.5\r\n" );
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document.write( "Edwin

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