document.write( "Question 457843: Simplify 9log(base27)(x) - 4log(base9)(x)\r
\n" ); document.write( "\n" ); document.write( "I didn't know how to type in a base for the logs, but i hope you can understand what I mean by (base27)
\n" ); document.write( "I tried by having logx^9/log27 - logx^4/logx but I didn't get anywhere... \n" ); document.write( "

Algebra.Com's Answer #314073 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+9%2Alog%2827%2Cx%29+-+4%2Alog%289%2Cx%29+\"$
\n" ); document.write( "(1) $\"+9%2Alog%283%5E3%2Cx%29+-+4%2Alog%283%5E2%2Cx%29+\"$
\n" ); document.write( "I'll say
\n" ); document.write( " $\"+log%283%5E3%2Cx%29+=+j+\"$
\n" ); document.write( " $\"+log%283%5E2%2Cx%29+=+k+\"$
\n" ); document.write( "Then
\n" ); document.write( " $\"%283%5E3%29%5Ej+=+x+\"$
\n" ); document.write( " $\"+x+=+3%5E%283j%29+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"%283%5E2%29%5Ek+=+x+\"$
\n" ); document.write( " $\"+x+=+3%5E%282k%29+\"$
\n" ); document.write( "then
\n" ); document.write( " $\"+3%5E%283j%29+=+3%5E%282k%29+\"$
\n" ); document.write( " $\"+3j+=+2k+\"$
\n" ); document.write( " $\"+j+=+%282%2F3%29%2Ak+\"$
\n" ); document.write( "go back to (1)
\n" ); document.write( "(1) $\"+9%2Alog%283%5E3%2Cx%29+-+4%2Alog%283%5E2%2Cx%29+\"$
\n" ); document.write( "(1) $\"+9%2A%282%2F3%29%2Ak+-+4k+\"$
\n" ); document.write( "(1) $\"+6k+-+4k+=+2k+\"$
\n" ); document.write( " $\"+2%2Alog%289%2Cx%29+\"$ answer
\n" ); document.write( "check answer:
\n" ); document.write( "Let $\"+x+=+27+\"$
\n" ); document.write( " $\"+9%2Alog%2827%2Cx%29+-+4%2Alog%289%2Cx%29+\"$
\n" ); document.write( " $\"+9%2Alog%2827%2C27%29+-+4%2Alog%289%2C27%29+\"$
\n" ); document.write( " $\"+9%2A1+-+4%2A%283%2F2%29+=+9-6+\"$
\n" ); document.write( " $\"+9+-+6+=+3+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+2%2Alog%289%2Cx%29+\"$
\n" ); document.write( " $\"+2%2Alog%289%2C27%29+\"$
\n" ); document.write( " $\"+2%2A%283%2F2%29+=+3+\"$ OK \r
\n" ); document.write( "
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\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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