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16.4x+2-16.2x+1+1=0 |
| Answer» {tex}16.4\\ ^ {x+2}-16.2\\ ^ {x+1}+1=0{/tex}{tex}16(4\\ ^ x\\times4\\ ^2)-16(2\\ ^ x\\times2\\ ^1)+1=0{/tex}{tex}16\\times16\\times4\\ ^x-16\\times2\\times2\\ ^x+1=0{/tex}{tex}256\\times4\\ ^ x-32\\times2\\ ^x+1=0{/tex}{tex}256\\times(2\\times2)\\ ^ x-32\\times2\\ ^ x+1=0{/tex}Let,{tex}2\\ ^x=p{/tex}{tex}256\\times p\\times p-32\\times p+1=0{/tex}{tex}256p\\ ^2-32p+1=0{/tex}{tex}256p\\ ^2-16p-16p+1=0{/tex}{tex}16p(16p-1)-1(16p-1)=0{/tex}{tex}(16p-1)(16p-1)=0{/tex}Either\xa0{tex}16p-1=0{/tex},or,{tex}16p-1=0{/tex}{tex}p={1\\over16},{1\\over16}{/tex}Now,\xa0{tex}p=2\\ ^ x{/tex}{tex}{1\\over 16}={ 2\\ ^ x}{/tex}, {tex}({1\\over2})\\ ^ 4=2\\ ^ x{/tex}{tex}(2)\\ ^ {-4}=2\\ ^ x{/tex}{tex}x= -4{/tex} | |