Solve For X LOG4 X10LOG4X23 Solve For X LOG3 X5LOG3X32Soluti

Solve For X: LOG_4 (X+10)+LOG_4(X-2)=3 Solve For X: LOG_3 (X+5)-LOG_3(X-3)=2

9)log₄(x+10) +log₄(x-2) =3

by properties of logaritham log a +log b =log ab

log₄(x+10)(x-2) =3

by properties of logaritham log_b a =c => a=b^c

(x+10)(x-2) =4³

(x²+8x-20) =64

x²+8x-84=0

x²+14x-6x-84=0

(x+14)(x-6)=0

x=-14, x=6

x cannot be less than 2 as terms inside the logarithams becomes negative

so x=6 is the answer

10)

log₃(x+5) -log₃(x-3) =2

by properties of logaritham log a -log b =log a/b

log₃(x+5)/(x-3) =2

by properties of logaritham log_b a =c => a=b^c

(x+5)/(x-3) =3²

(x+5)/(x-3) =9

(x+5)=9(x-3)

x+5 =9x-27

9x -x =5+27

8x=32

x=4