to find x
logb(x)=2/3logb(8)+1/2logb(9)-logb(6)
2007-11-26 22:10:30 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
logb(x)=2/3logb(8)+1/2logb(9)-logb(6)
=> logb(x)=2/3logb(2^3)+1/2logb(3^2)-logb(2*3)
=> logb(x)=2logb(2)+logb(3)-[logb(2)-logb(3)]
=> logb(x)=2logb(2)+logb(3)-logb(2)+logb(3)
=> logb(x)=logb(2)+2logb(3)
=> logb(x)=logb(2)+logb(3^2)
=> logb(x)=logb(2)+logb(9)
=> logb(x)=logb(2*9)
=> logb(x)=logb(18)
=> x = 18
2007-11-26 22:29:00 · answer #1 · answered by sulinderkumarsharma 2 · 0⤊ 2⤋
let log = log b in the following:-
log x = (2/3) log 8 + (1/2) log 9 - log 6
log x = log 8^(2/3) + log 9^(1/2) + log 6^(-1)
log x = log [ 8^(2/3) 9^(1/2) 6^(-1) ]
x = [ 8^(2/3) 9^(1/2) 6^(-1) ]
x = 4 x 3 x 1 / 6
x = 2
2007-11-27 11:35:24 · answer #2 · answered by Como 7 · 3⤊ 1⤋
log(b)x=log(b)4+log(b)3-lob(b)6
log(b)x=log(b)2
x=2
2007-11-27 06:24:07 · answer #3 · answered by someone else 7 · 1⤊ 0⤋
logb(x)=2/3logb(8)+1/2logb(9)-logb(6)
logb(x)=logb(8^2/3)+logb(9^1/2)-logb(6)
logb(x)=logb(4)+logb(3)-logb(6)
logb(x)=logb(4*3)-logb(6)
logb(x)=logb(12)-logb(6)
logb(x)=logb(12/6)
logb(x)=logb(2)
x=2
2007-11-27 06:36:46 · answer #4 · answered by picaresque_82 2 · 0⤊ 1⤋