LOGARITHMS 4

If log₂₅x + log₂₅(x-24)=1; find x.

Solution

log₂₅x + log₂₅(x-24)=1

log₂₅x(x-24)=1

log₂₅(x²-24x)=1

 x²-24x=25¹

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 log₁₆x + log₁₆(3x-4)=¹/2; find x.