document.write( "Question 250423: Express as a single logarithm, and, if possible, simplify??\r
\n" ); document.write( "\n" ); document.write( "4 loga y + 1/7 loga z\r
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Algebra.Com's Answer #182377 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
the rules of logarithms state:\r
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\n" ); document.write( "\n" ); document.write( "\"log%28a%2Ab%29+=+log%28a%29+%2B+log%28b%29\" (rule 1)\r
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\n" ); document.write( "\n" ); document.write( "\"log%28a%2Fb%29+=+log%28a%29+-+log%28b%29\" (rule 2)\r
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\n" ); document.write( "\n" ); document.write( "\"log%28a%5Eb%29+=+b+%2A+log%28a%29\" (rule 3)\r
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\n" ); document.write( "\n" ); document.write( "your expression is:\r
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\n" ); document.write( "\n" ); document.write( "\"4+%2A+log%28a%2Cy%29+%2B+%281%2F7%29+%2A+log%28a%2Cz%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"4+%2A+log%28a%2Cy%29+=+log%28a%2Cy%5E4%29\" by rule 3.\r
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\n" ); document.write( "\n" ); document.write( "\"%281%2F7%29+%2A+log%28a%2Cz%29+=+log%28a%2Cz%5E%281%2F7%29%29\" by rule 3.\r
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\n" ); document.write( "\n" ); document.write( "your expression becomes:\r
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\n" ); document.write( "\n" ); document.write( "\"log%28a%2Cy%5E4%29+%2B+log%28a%2Cz%5E%281%2F7%29%29\"\r
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\n" ); document.write( "\n" ); document.write( "this becomes \"log%28a%2C%28y%5E4%2Az%5E%281%2F7%29%29%29\" by rule 1.\r
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\n" ); document.write( "\n" ); document.write( "since \"z%5E%281%2F7%29\" can also be written as \"root%287%2Cz%29\", this can also be written as:\r
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\n" ); document.write( "\n" ); document.write( "\"log%28a%2C%28y%5E4%2Aroot%287%2Cz%29%29%29\"\r
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\n" ); document.write( "\n" ); document.write( "you can prove that your original expression of \"4+%2A+log%28a%2Cy%29+%2B+%281%2F7%29+%2A+log%28a%2Cz%29\" is the same as your final expression of \"log%28a%2C%28y%5E4%2Aroot%287%2Cz%29%29%29\" by substituting for the values of a, y, z.\r
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\n" ); document.write( "\n" ); document.write( "I used a = 10 because this base is solvable by using the LOG function of the calculator.\r
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\n" ); document.write( "\n" ); document.write( "I let y = 7
\n" ); document.write( "I let z = 15\r
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\n" ); document.write( "\n" ); document.write( "I got the same answer for the original expression and the final expression which says that I made the translation correctly.\r
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