document.write( "Question 202664: could sombody help me to solve it?\r
\n" ); document.write( "\n" ); document.write( "1/3.log(20,2x-1)=log(20,11)-2.log(20,(2x-1)^(1/3))+log(5,(log7,7)) \n" ); document.write( "

Algebra.Com's Answer #152846 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Quick note: $\"log%287%2C%287%29%29=1\"$ and $\"log%285%2C%281%29%29=0\"$ . So $\"log%285%2C%28log%287%2C%287%29%29%29%29=log%285%2C%281%29%29=0\"$ . In other words, $\"log%285%2C%28log%287%2C%287%29%29%29%29=0\"$ \r
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\n" ); document.write( "\n" ); document.write( "So the expression

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\n" ); document.write( "\n" ); document.write( "simplifies to

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Start with the given expression.\r
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Rewrite the last log using the identity $\"log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29\"$ \r
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Multiply\r
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Subtract $\"log%2820%2C%2811%29%29\"$ from both sides.\r
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Subtract $\"%281%2F3%29log%2820%2C%282x-1%29%29\"$ from both sides.\r
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\n" ); document.write( "\n" ); document.write( " $\"-log%2820%2C%2811%29%29=%28-2%2F3-1%2F3%29log%2820%2C%282x-1%29%29\"$ Factor out the GCF $\"log%2820%2C%282x-1%29%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"-log%2820%2C%2811%29%29=%28-3%2F3%29log%2820%2C%282x-1%29%29\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( " $\"-log%2820%2C%2811%29%29=-log%2820%2C%282x-1%29%29\"$ Reduce\r
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\n" ); document.write( "\n" ); document.write( " $\"log%2820%2C%2811%29%29=log%2820%2C%282x-1%29%29\"$ Multiply both sides by -1\r
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\n" ); document.write( "\n" ); document.write( " $\"11=2x-1\"$ Since the bases of the logs are equal, this means that the arguments are equal.\r
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\n" ); document.write( "\n" ); document.write( " $\"11%2B1=2x\"$ Add 1 to both sides.\r
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\n" ); document.write( "\n" ); document.write( " $\"12=2x\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( " $\"12%2F2=x\"$ Divide both sides by 2 to isolate \"x\".\r
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\n" ); document.write( "\n" ); document.write( " $\"6=x\"$ Reduce\r
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\n" ); document.write( "\n" ); document.write( " $\"x=6\"$ Rearrange the equation.\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So the solution is $\"x=6\"$ \r
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