Tentukan nilai x daripertidaksamaanberikut! ( 4 lo g x ) 2 + 4 lo g x − 2 < 0

Pembahasan

Ingat bahwa! Syarat numerus pada logaritma. a lo g f ( x ) , dengan f ( x ) > 0 Sehingga nilai x dapat ditentukan dengan cara berikut ( 4 lo g x ) 2 + 4 lo g x − 2 < 0 Misalkan p = 4 lo g x , maka p 2 + p − 2 < 0 ( p + 2 ) ( p − 1 ) < 0 p = − 2 atau p = 1 − 2 < p < 1 Untuk p > − 2 &-2\\{}^4\log\;x&>&-2\\x&>&4^{-2}\\x&>&\frac1{16}\;.........{\color[rgb]{0.0, 0.0, 1.0}1}{\color[rgb]{0.0, 0.0, 1.0})}\end{array}" data-mathml="«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«mi»p«/mi»«/mtd»«mtd»«mo»§#62;«/mo»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mmultiscripts»«mi»log«/mi»«mprescripts/»«none/»«mn»4«/mn»«/mmultiscripts»«mo»§#160;«/mo»«mi»x«/mi»«/mtd»«mtd»«mo»§#62;«/mo»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»x«/mi»«/mtd»«mtd»«mo»§#62;«/mo»«/mtd»«mtd»«msup»«mn»4«/mn»«mrow»«mo»-«/mo»«mn»2«/mn»«/mrow»«/msup»«/mtd»«/mtr»«mtr»«mtd»«mi»x«/mi»«/mtd»«mtd»«mo»§#62;«/mo»«/mtd»«mtd»«mfrac»«mn»1«/mn»«mn»16«/mn»«/mfrac»«mo»§#160;«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mn mathcolor=¨#0000FF¨»1«/mn»«mo mathcolor=¨#0000FF¨»)«/mo»«/mtd»«/mtr»«/mtable»«/math»" role="math" src="data:image/png;base64,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" style="max-width: none;"> Untuk p < 1 Syarat numerusnya. 0\;.......{\color[rgb]{0.0, 0.0, 1.0}3}{\color[rgb]{0.0, 0.0, 1.0})}" data-mathml="«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#62;«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mn mathcolor=¨#0000FF¨»3«/mn»«mo mathcolor=¨#0000FF¨»)«/mo»«/math»" role="math" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFgAAAAWCAYAAABEx1soAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAclJREFUeNrtl71Lw0AYxoNIESmCSBBxEIqjiCClhFL8B8TVWdwdXIqDg4OLoxQXESc3hw4dBJEi4iCIOJaAQxEHcRWRIJzPmdevy6X5MEEP3wd+lLy5j+bJm/fuLIuVocSaDytPkw/AQhYjnYJqin6yzxXwwDWoGWQejBOXAP9dPIEjUFbajAAXFH46mwNOEhpdAh0wS9fy16W4CQY3QQX0gX6wArqadttgOatZvxrtRLRtAHXiJYqbWA6kyQ+a+Dw4VKNNxaBhcAzGEhrd7mH0DbCVGD4pq2uYsTKDp8Geb2bg/qDO+HGA+mKhsyXrh3wDkylmX5UzhNx7CYl7BpkriFsw0aOd9pnqxD6YSVEq2hEZHGbws4EZ7PhlQNbk+AaXyIS5FMaexajBrqZE2FQ6TKzBtr9jCMSL4N7SPOg5WAQbCY2Nu9Vq0KKmLnI7hhosM/kxziJXpAVtiq53QTli9CTGqtu09/JToezttU1rEX8gJlqfJUEMgS1/SxYwGIkkPhKpQANVlZX9Agzk8NprdMDw6MAR9ZKEZtH8pdhbZsqDBsqouAOb/lbtW5tR0MnioMHK+ajMCpq7DursA4vFYrFYLBbrv+sV7pWvPJtziiAAAADxdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPng8L21pPjxtbz4mZ3Q7PC9tbz48bW4+MDwvbW4+PG1vPiYjeEEwOzwvbW8+PG1vPi48L21vPjxtbz4uPC9tbz48bW8+LjwvbW8+PG1vPi48L21vPjxtbz4uPC9tbz48bW8+LjwvbW8+PG1vPi48L21vPjxtbiBtYXRoY29sb3I9IiMwMDAwRkYiPjM8L21uPjxtbyBtYXRoY29sb3I9IiMwMDAwRkYiPik8L21vPjwvbWF0aD6G90yJAAAAAElFTkSuQmCC" style="max-width: none;"> Dari 1, 2, dan 3 diperoleh sebagai berikut. { 16 1 ​ < x < 4 } Dengan demikian himpunan penyelesaiandari pertidaksamaanlogaritma tersebut adalah { x ∣ 16 1 ​ < x < 4 , x ∈ R }