SOLUTION: Solve for x:log 16 base x÷log x base 16=3

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Question 736028: Solve for x:log 16 base x÷log x base 16=3
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:log 16 base x÷log x base 16=3
log%28x%2C%2816%29%29%2Flog%2816%2C%28x%29%29=%283%29
Convert to base(10)
%28log%2816%29%2Flog%28x%29%29%2F%28log%28x%29%2Flog%2816%29%29=%283%29
%28%28log%2816%29%29%5E2%29%2F%28%28log%28x%29%29%5E2%29=%283%29%29
take sqrt of both sides:
%28log%2816%29%29%2F%28log%28x%29%29=sqrt%283%29%29
log(16)=√3log(x)
log(x)=log(16)/√3≈0.6952
x=10^0.6962≈4.9568
..
Check:
log(16) basex≈1.732
logx base(16)≈0.5773
(1.732/0.5773≈2.999..≈3