using the properties of logs, we have
log 5(x+2)/(x-1) = 2
5(x+2)/(x-1) = 100
Now finish it off
Log 10 5 + log 10 ( x + 2 ) - log 10 ( x - 1 ) = 2
2 answers
Log 5+log (x+2)- log (x-1) =log 100 since log 100=2
log 5(x+2)= log (5x+10) since log a+log b =log ab
log (5x+10)/(x-1) since log a-log b= log a/b
log (5x+10)/(x-1)= log 100
(5x+10)/(x-1)= 100
5x+10= 100(x-1)
5x+10= 100x-100
10+100= 100x-5x
110=95x
x=110/95
x=1 3/19
log 5(x+2)= log (5x+10) since log a+log b =log ab
log (5x+10)/(x-1) since log a-log b= log a/b
log (5x+10)/(x-1)= log 100
(5x+10)/(x-1)= 100
5x+10= 100(x-1)
5x+10= 100x-100
10+100= 100x-5x
110=95x
x=110/95
x=1 3/19