document.write( "Question 991960: log4 (x-3)-log16 (x-3)=1 \n" ); document.write( "

Algebra.Com's Answer #611789 by ikleyn(52814) $\"\"$ $\"About$

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\n" ); document.write( " $\"log%284%2C%28x-3%29%29\"$ - $\"log%2816%2C%28x-3%29%29\"$ = $\"1\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Notice that $\"log%2816%2C%28x-3%29%29\"$ = $\"1%2F2\"$ $\"log%284%2C%28x-3%29%29\"$ ,     since      $\"16\"$ = $\"4%5E2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "So your equation takes the form\r
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\n" ); document.write( "\n" ); document.write( " $\"log%284%2C%28x-3%29%29\"$ - $\"1%2F2\"$ $\"log%284%2C%28x-3%29%29\"$ = $\"1\"$ ,     or      $\"1%2F2\"$ $\"log%284%2C%28x-3%29%29\"$ = 1,     or      $\"log%284%2C%28x-3%29%29\"$ = $\"2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "The last equation means that \r
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\n" ); document.write( "\n" ); document.write( " $\"log%282%2C%28x-3%29%29\"$ = $\"4\"$ ,     since      $\"4\"$ = $\"2%5E2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Hence, x - 3 = $\"2%5E4\"$ = 16 and then x = 19.\r
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\n" ); document.write( "\n" ); document.write( "Answer. x = 19.\r
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