Question

Solve the equatio, lg(1-2x)-2lgx=1-lg(2-5x)

Answer 1

Answer:

$log(1 - 2x) - 2 log(x) = 1 - log(2 - 5x) \\ \\ log(1 - 2x) - log( {x}^{2} ) = log(10) - log(2 - 5x) \\ \\ log( \frac{1 - 2x}{ {x}^{2} } ) = log(\frac{ 10}{2 - 5x} ) \\ \\ ( \frac{1 - 2x}{ {x}^{2} } ) = (\frac{ 10}{2 - 5x} ) \\ \\ (2 - 5x)(1 - 2x) = 10 {x}^{2} \\ \\ 2 - 2x - 5x + 10 {x}^{2} = 10 {x}^{2} \\ \\ 7x = 2 \\ \\ x = \frac{2}{7}$

Answer 2

Answer:

log(1−2x)−2log(x)=1−log(2−5x)log(1−2x)−log(x2)=log(10)−log(2−5x)log(x21−2x)=log(2−5x10)(x21−2x)=(2−5x10)(2−5x)(1−2x)=10x22−2x−5x+10x2=10x27x=2x=72