LOGARITHMS 16

If log₅x + log₅(x-24)=2; find x.

solution

log₅x + log₅(x-24)=2

log₅x(x-24)=2

log₅(x²-24x)=2

 x²-24x=5²

x²-24x=25

x²-24x - 25=0

We factorize by splitting the middle term: -24x = +x – 25x

x²+x-25x - 25=0

(x²+x)-(25x – 25)=0

x(x+1) - 25(x + 1)=0

 (x+1) (x- 25) = 0

x+1=0  OR  x- 25 = 0

x =-1  OR  x= 25

Hence x =-1  OR  x= 25

TRY THIS……………

If log₄x + log₄(3x-4)=1; find x.