solve each equation using log a 4x2 25x 8 b log7x 12 2logxS

solve each equation (using log)

(a) 4^x² .2^5x = 8

(b) log(7x- 12)= 2logx

Solution

a)4^{x^2}*2^5x=8

apply log on both sides

log(4^{x^2}*2^5x)=log8

log(4^{x^2})+log(2^5x)=log2³

log(2^{2x^2})+log(2^5x)=log2³

2x²log2+ 5xlog2=3log2

(2x²+ 5x)log2=3log2

2x²+ 5x=3

2x²+ 5x-3=0

2x²+ 6x-x-3=0

(2x-1)(x+3)=0

x=1/2 ,x=-3

b)log(7x- 12)= 2logx

log(7x- 12)= logx²

(7x- 12)= x²

x²-7x+12=0

(x-3)(x-4)=0

x =3, x=4