SOLUTION: Find x {{{ log( sqrt (x), 3 ) + log( x^2, 16 ) =1 }}}

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Question 792472: Find x +log%28+sqrt+%28x%29%2C+3+%29+%2B++log%28+x%5E2%2C+16+%29+=1+
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
+log%28+sqrt+%28x%29%2C+3+%29+%2B++log%28+x%5E2%2C+16+%29+=1+
Expressing everything using base 10 logarithms, we get
log%283%29%2Flog%28sqrt%28x%29%29%2Blog%2816%29%2Flog%28%28x%5E2%29%29=1 ---> log%283%29%2Flog%28%28x%5E0.5%29%29%2Blog%2816%29%2Flog%28%28x%5E2%29%29=1 ---> log%283%29%2F%280.5%2Alog%28x%29%29%2Blog%2816+%29%2F%282%2Alog%28x%29%29=1 --->

2%2Alog%28+3+%29%2Flog+%28x%29+%2B+0.5log%28+16+%29%2Flog%28+x%29+=1+ ---> %282%2Alog%28+3+%29%2B+0.5%2Alog%28+16+%29%29%2Flog%28+x%29+=1+ ---> %28log%28%283%5E2%29%29%2B+log%28%2816%5E0.5%29%29%29%2Flog%28+x%29+=1+ --->

%28log%289%29%2Blog%284%29%29%2Flog%28x%29=1 ---> log%28%289%2A4%29%29%2Flog%28x%29=1 ---> log%2836%29%2Flog%28x%29+=1+ --->

log%2836%29=log%28x%29 --> 36=x