SOLUTION: I am in desperate need of help with a logarithm problem. It is as follows: 1/logbase2(x)+1/logbase3(x)+1/logbase4(x)+1/logbase6(x)=4 Solve for x. Thank you so much for th

Question 493430: I am in desperate need of help with a logarithm problem. It is as follows:
1/logbase2(x)+1/logbase3(x)+1/logbase4(x)+1/logbase6(x)=4
Solve for x.
Thank you so much for the help!
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
1/logbase2(x)+1/logbase3(x)+1/logbase4(x)+1/logbase6(x)=4
Solve for x.
**
convert to base 10
log(2)/log(x)+log(3)/log(x)+log(4)/log(x)+log(6)/log(x)=4
log[(2)+log(2)+log(2)+log(2)]/log(x)=4
log(2*3*4*6)/log(x)=4
log(144)=4log(x)=log(x^4)
144=x^4
take 4th root of both sides
x=(12^2)^1/4=√12=3.4641
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