SOLUTION: Could you possible help me write the following equation as a single number or expression? {{{ 1/3 log base b of 27 + 2 log base b of 6 - 1/2 log base b 144 }}} much obliged

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Question 126770This question is from textbook Algebra 2 Explorations and Applications
: Could you possible help me write the following equation as a single number or expression?
+1%2F3+log+base+b+of+27+%2B+2+log+base+b+of+6+-+1%2F2+log+base+b+144+

much obliged, courtney reneeThis question is from textbook Algebra 2 Explorations and Applications

Answer by solver91311(12126) About Me  (Show Source):
You can put this solution on YOUR website!
+%281%2F3%29%2Alog%28b%2C27%29+%2B+2+%2Alog%28b%2C+6%29+-+%281%2F2%29+%2Alog%28b%2C+144%29+



Rule 1: n%2Alog%28b%2Cx%29=log%28b%2Cx%5En%29

Rule 2: x%5E%281%2Fn%29=root%28n%2Cx%29

Rule 3: log%28b%2Cx%29%2Blog%28b%2Cy%29=log%28b%2Cxy%29

Rule 4: log%28b%2Cx%29-log%28b%2Cy%29=log%28b%2Cx%2Fy%29

Let's start by applying Rule 1:
log%28b%2C27%5E%281%2F3%29%29+%2Blog%28b%2C+6%5E2%29+-+log%28b%2C+144%5E%281%2F2%29%29+

Now Rule 2:
log%28b%2Croot%283%2C27%29%29+%2Blog%28b%2C+6%5E2%29+-+log%28b%2C+sqrt%28144%29%29+

And do the arithmetic:
log%28b%2C3%29+%2Blog%28b%2C36%29+-+log%28b%2C12%29+

Now Rule 3:
log%28b%2C3%2A36%29-log%28b%2C12%29

Now Rule 4:
log%28b%2C%283%2A36%29%2F12%29

And simplify:
log%28b%2C9%29