Please do all of them I dont understand these problems 41 lo

Please do all of them! I dont understand these problems.

Solution

41)log2 -(1/2)log9 +3log3 =x

by properties of logaritham m(log(a))=log(a^m)

log2 -log9^1/2 +log3³ =x

log2 -log3 +log27 =x

by properties of logaritham log(a)+log(b)=log(ab), log(a)-log(b)=log(a/b)

log(2*27/3) =x

log(18)=x

x=log(18)

45)log_bx -(1/2)log_b2 =(1/2)log_b(3x-4)

log_bx -log_b2^1/2 =log_b(3x-4)^1/2

log_b(x/2^1/2)=log_b(3x-4)^1/2

(x/2^1/2)=(3x-4)^1/2

squaring on both sides

(x²/2)=(3x-4)

x²=6x-8

x²-6x+8=0

(x-2)(x-4)=0

x=2 ,x=4