document.write( "Question 115571: i really don't know where to begin with this problem at all?
\n" ); document.write( "given log base a 2= 0.431 and log base a 3= 0.683 find the following ....
\n" ); document.write( "log base a 6 and log base a 81 and log base a 2a?\r
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\n" ); document.write( "\n" ); document.write( "if you could help me it would be great thank you ! \n" ); document.write( "
Algebra.Com's Answer #84118 by bucky(2189)\"\" \"About 
You can put this solution on YOUR website!
You need to know a couple of properties of logarithms.
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\n" ); document.write( "One of the properties is the multiplication property: \"log%28a%2C+x%2Ay%29+=+log%28a%2Cx%29+%2B+log%28a%2Cy%29\"
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\n" ); document.write( "The first problem is to find \"log%28a%2C6%29\". Note that 6 is equal to 2*3. So you can re-write
\n" ); document.write( "the problem as \"log%28a%2C2%2A3%29\" But the property of logs described above converts this to:
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\n" ); document.write( " \"log%28a%2C2%29+%2B+log%28a%2C3%29\"
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\n" ); document.write( "Both of these logs are given ... \"log%28a%2C2%29+=+0.341\" and \"log%28a%2C3%29+=+0.683\" Inserting
\n" ); document.write( "these values into the problem results in:
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\n" ); document.write( "\"log%28a%2C2%2A3%29=log%28a%2C2%29+%2B+log%28a%2C3%29=+0.341+%2B+0.683+=+1.024\"
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\n" ); document.write( "So the answer is \"log%28a%2C6%29+=+1.024\"
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\n" ); document.write( "The next problem uses the exponent property that \"log%28a%2Cm%5En%29+=+n%2Alog%28a%2Cm%29\"
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\n" ); document.write( "The problem is to find the value of \"log%28a%2C81%29\". To do that you can recognize that
\n" ); document.write( "\"81+=+3%5E4\". If you substitute that into the problem, you get:
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\n" ); document.write( "\"log%28a%2C81%29+=+log%28a%2C3%5E4%29\"
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\n" ); document.write( "Next apply the exponent property to add another step to the problem:
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\n" ); document.write( "\"log%28a%2C81%29+=+log%28a%2C3%5E4%29+=+4%2Alog%28a%2C3%29\"
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\n" ); document.write( "Finally add the last step by substituting 0.683 for \"log%28a%2C3%29\":
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\n" ); document.write( "\n" ); document.write( "\"log%28a%2C81%29+=+log%28a%2C3%5E4%29+=+4%2Alog%28a%2C3%29=+4%2A0.683+=+2.732\"
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\n" ); document.write( "So the answer to this second problem is \"log%28a%2C81%29+=+2.732\"
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\n" ); document.write( "The final problem is:
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\n" ); document.write( "\"log%28a%2C2%2Aa%29\"
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\n" ); document.write( "Use the multiplication property to split this into two logarithms as follows:
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\n" ); document.write( "\"log%28a%2C2%2Aa%29=log%28a%2C2%29%2Blog%28a%2Ca%29\"
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\n" ); document.write( "Another property is that for any base if you take the logarithm of the base, the answer is 1.
\n" ); document.write( "This means \"log%28a%2Ca%29+=+1\". Plus you are given that \"log%28a%2C2%29+=+0.431\". Making these
\n" ); document.write( "two substitutions results in:
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\n" ); document.write( "\"log%28a%2C2%2Aa%29=log%28a%2C2%29%2Blog%28a%2Ca%29=0.431+%2B+1+=+1.431\".
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\n" ); document.write( "So the answer to this problem is: \"log%28a%2C2%2Aa%29+=+1.431\"
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\n" ); document.write( "Hope this helps you to gain some insight into a couple of properties of logarithms. It's
\n" ); document.write( "sort of late to be doing math, so be sure to check the math in these problems. Mistakes
\n" ); document.write( "have a tendency to creep into late-night work ... but the basic principles involving the
\n" ); document.write( "properties of logarithms are correct.
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