If `(log)_4A=(log)_6B=(log)_9(A+B),t h e n` `[4(B/A)]` (where [ ] represents the greatest integer function) equals ..............

Explanation

`log_4^A=log_6^B=log_9^(A+B)=x`

`A=4^x,B=6^x,A+B=9^x`

`4^x+6^x=9^x`

`3^(2x)-2^x*3^x-2^(2x)=0`

`(3/2)^(2x)-(3/2)^x-1=0`

`(3/2)^x=(1pmsqrt(1+4))/2=(1+sqrt5)/2`

`(4B/A)=[2(1+sqrt5)]`

`=[2(1+2.23)]`

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