document.write( "Question 1153082: https://imgur.com/a/nHNVzJD Find log(base z)w \n" ); document.write( "
Algebra.Com's Answer #775260 by MathLover1(20850)\"\" \"About 
You can put this solution on YOUR website!
\"log%28x%2Cw%29=24\"\r
\n" ); document.write( "\n" ); document.write( "\"log%28y%2Cw%29=40\"\r
\n" ); document.write( "\n" ); document.write( "\"log%28xyz%2Cw%29=12\"
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\n" ); document.write( "\n" ); document.write( "\"log%28x%2Cw%29=24\"\r
\n" ); document.write( "\n" ); document.write( "\"log%28w%29%2Flog%28x%29=24\"\r
\n" ); document.write( "\n" ); document.write( "\"log%28w%29=24log%28x%29\"\r
\n" ); document.write( "\n" ); document.write( "\"log%28w%29=log%28x%5E24%29\"\r
\n" ); document.write( "\n" ); document.write( "\"w=x%5E24\".....eq.1a\r
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\n" ); document.write( "\n" ); document.write( "\"log%28y%2Cw%29=40\"\r
\n" ); document.write( "\n" ); document.write( "\"log%28w%29%2Flog%28y%29=40\"\r
\n" ); document.write( "\n" ); document.write( "\"log%28w%29=40log%28y%29\"\r
\n" ); document.write( "\n" ); document.write( "\"log%28w%29=log%28y%5E40%29\"\r
\n" ); document.write( "\n" ); document.write( "\"w=y%5E40\"....eq.2a\r
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\n" ); document.write( "\n" ); document.write( "\"log%28xyz%2Cw%29=12\"\r
\n" ); document.write( "\n" ); document.write( "\"log%28w%29%2Flog%28xyz%29=12\"\r
\n" ); document.write( "\n" ); document.write( "\"log%28w%29=12log%28xyz%29\"\r
\n" ); document.write( "\n" ); document.write( "\"log%28w%29=log%28%28xyz%29%5E12%29\"\r
\n" ); document.write( "\n" ); document.write( "\"w=%28xyz%29%5E12\"....eq.3a\r
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\n" ); document.write( "\n" ); document.write( "from 1a and 2a we have \r
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\n" ); document.write( "\n" ); document.write( "\"x%5E24=y%5E40\"\r
\n" ); document.write( "\n" ); document.write( "\"x=root%2824%2C%28y%5E40%29%29\"\r
\n" ); document.write( "\n" ); document.write( "\"x+=+2sqrt%286%29%2Asqrt%28y%5E40%29\"..............1b\r
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\n" ); document.write( "\n" ); document.write( "from 1a and 3a we have\r
\n" ); document.write( "\n" ); document.write( "\"x%5E24=%28xyz%29%5E12\"\r
\n" ); document.write( "\n" ); document.write( "\"x=root%2824%2C%28xyz%29%5E12%29%29\"\r
\n" ); document.write( "\n" ); document.write( "\"x+=+2sqrt%286%29%2Ax%5E6%2Ay%5E6%2Az%5E6\".........2b\r
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\n" ); document.write( "\n" ); document.write( "from 2a and 3a we have\r
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\n" ); document.write( "\n" ); document.write( "\"y%5E40=%28xyz%29%5E12\"\r
\n" ); document.write( "\n" ); document.write( "\"y=root%2840%2C%28xyz%29%5E12%29\"\r
\n" ); document.write( "\n" ); document.write( "\"y+=+2sqrt%2810%29%2Asqrt%28x%5E12%2Ay%5E12%2Az%5E12%29\"\r
\n" ); document.write( "\n" ); document.write( "\"y+=+2sqrt%2810%29%2Ax%5E6%2Ay%5E6%2Az%5E6\"...........3b\r
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\n" ); document.write( "\n" ); document.write( "from 1b and 2b we have\r
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\n" ); document.write( "\n" ); document.write( "\"2sqrt%286%29%2Asqrt%28y%5E40%29=+2sqrt%286%29%2Ax%5E6%2Ay%5E6%2Az%5E6\"\r
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\n" ); document.write( "\n" ); document.write( "\"sqrt%28y%5E40%29=+x%5E6+%2Ay%5E6+%2Az%5E6\"\r
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\n" ); document.write( "\n" ); document.write( "\"y%5E20=+x%5E6+%2Ay%5E6+%2Az%5E6\"\r
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\n" ); document.write( "\n" ); document.write( "\"y=+root%2820%2C%28x%5E6+%2Ay%5E6+%2Az%5E6%29%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"y=2sqrt%285%29%2Asqrt%28x%5E6%2Ay%5E6%2Az%5E6%29\".......1c\r
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\n" ); document.write( "\n" ); document.write( "from 3b and 1c we have\r
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\n" ); document.write( "\n" ); document.write( "\"2sqrt%2810%29%2Ax%5E6%2Ay%5E6%2Az%5E6=2sqrt%285%29%2Asqrt%28x%5E6%2Ay%5E6%2Az%5E6%29\"\r
\n" ); document.write( "\n" ); document.write( "\"sqrt%2810%29%2Ax%5E6%2A+y%5E6%2A+z%5E6=sqrt%285%29%2Asqrt%28x%5E6%2Ay%5E6%2Az%5E6%29\"\r
\n" ); document.write( "\n" ); document.write( "\"%28x%5E6%2A+y%5E6%2A+z%5E6%29%2Fsqrt%28x%5E6+y%5E6+z%5E6%29=sqrt%285%29%2Fsqrt%2810%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"%28x%5E6%2A+y%5E6%2A+z%5E6%29%2Fsqrt%28x%5E6+y%5E6+z%5E6%29=1%2Fsqrt%282%29\".......square both sides\r
\n" ); document.write( "\n" ); document.write( "\"%28x%5E12%2A+y%5E12%2A+z%5E12%29%2F%28x%5E6+y%5E6+z%5E6%29=1%2F2\"\r
\n" ); document.write( "\n" ); document.write( "\"%28x%5E6%2A+y%5E6%2A+z%5E6%29=1%2F2\"...........2c\r
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\n" ); document.write( "\n" ); document.write( "go to\r
\n" ); document.write( "\n" ); document.write( "\"y=2sqrt%285%29%2Asqrt%28x%5E6+y%5E6+z%5E6%29\".......1c, use 2c\r
\n" ); document.write( "\n" ); document.write( "\"y=2sqrt%285%29%2Asqrt%281%2F2%29\"\r
\n" ); document.write( "\n" ); document.write( "\"y=2sqrt%285%29%2A1%2Fsqrt%282%29\"\r
\n" ); document.write( "\n" ); document.write( "\"y=sqrt%2810%29\"....................3c\r
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\n" ); document.write( "\n" ); document.write( "go to \r
\n" ); document.write( "\n" ); document.write( "\"x+=+2sqrt%286%29%2Ax%5E6+%2Ay%5E6+%2Az%5E6\".........2b, use 2c\r
\n" ); document.write( "\n" ); document.write( "\"x+=+2sqrt%286%29%2A%281%2F2%29\"\r
\n" ); document.write( "\n" ); document.write( "\"x+=+sqrt%286%29\"\r
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\n" ); document.write( "\n" ); document.write( "go to\r
\n" ); document.write( "\n" ); document.write( "\"x+=+2sqrt%286%29%2Ax%5E6+%2Ay%5E6+%2Az%5E6\".........2b, substitute \"x\" and\"+y\"\r
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\n" ); document.write( "\n" ); document.write( "\"sqrt%286%29+=+2sqrt%286%29%2A%28sqrt%286%29%29%5E6+%2A%28sqrt%2810%29%29%5E6+%2Az%5E6\"\r
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\n" ); document.write( "\n" ); document.write( "\"sqrt%286%29+=+432sqrt%286%29+%2A1000%2Az%5E6\"\r
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\n" ); document.write( "\n" ); document.write( "\"z%5E6=sqrt%286%29%2F%28432sqrt%286%29+%2A1000%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"z%5E6=1%2F432000\"\r
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\n" ); document.write( "\n" ); document.write( "\"z=root%286%2C%281%2F432000%29%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"z=sqrt%285%29%2F600\"\r
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\n" ); document.write( "\n" ); document.write( "now find base \"xyz\":\r
\n" ); document.write( "\n" ); document.write( "\"xyz=+sqrt%286%29%2A+sqrt%2810%29%2A%28sqrt%285%29%2F600%29\"\r
\n" ); document.write( "\n" ); document.write( "\"xyz=+sqrt%283%29%2F60\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "go to \"log%28xyz%2Cw%29=12\"......eq.3, substitute \"xyz\"\r
\n" ); document.write( "\n" ); document.write( " \"log%28sqrt%283%29%2F60%2Cw%29=12\"\r
\n" ); document.write( "\n" ); document.write( "\"log%28w%29%2Flog%28sqrt%283%29%2F60%29=12\"\r
\n" ); document.write( "\n" ); document.write( "\"log%28w%29=12log%28sqrt%283%29%2F60%29\"\r
\n" ); document.write( "\n" ); document.write( "\"log%28w%29=log%28%28sqrt%283%29%2F60%29%5E12%29\".....if log same\r
\n" ); document.write( "\n" ); document.write( "\"w=%28sqrt%283%29%2F60%29%5E12\".........3c\r
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\n" ); document.write( "\n" ); document.write( "then \"log%28z%2Cw%29\" will be\r
\n" ); document.write( "\n" ); document.write( "\"log%28z%2Cw%29=log%28%28sqrt%283%29%2F60%29%5E12%29%2Flog%28sqrt%285%29%2F600%29%29\"\r
\n" ); document.write( "\n" ); document.write( "\"log%28z%2Cw%29=%2812+log%281200%29%29%2Flog%2872000%29\"\r
\n" ); document.write( "\n" ); document.write( "\"log%28z%2Cw%29=7.6\"\r
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