1) Let's take logarithm of both sides of equation:
log(4x−2)=log(3x+4),(x−2)⋅log(4)=(x+4)⋅log(3),xlog(4)−2log(4)=xlog(3)+4log(3),xlog(4)−xlog(3)=4log(3)+2log(4),x(log(4)−log(3))=4log(3)+2log(4),x(log(34))=log(81)+log(16),x(log(34))=log(1296),x=log(34)log(1296).Answer:
x=log(34)log(1296).
2)
9x−3x−8=0,32x−3x−8=0.Let 3x=y, then we get the following quadratic equation:
y2−y−8=0.This quadratic equation has two roots:
y1=2a−b+b2−4ac=21+33,y2=2a−b−b2−4ac=21−33.Let's go back, substitute y and solve for x:
3x=21+33,log(3x)=log(21+33),xlog(3)=log(21+33),x=log(3)log(21+33).There is no solution for case when we substitute y2=21−33.
Answer:
x=log(3)log(21+33).
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