Question

log (10x^2+5)-2log(1-x)=1

Answer 1

log (10x² + 5) - 2log (1 - x) = 1
log (10x² + 5) - log (1 - x)² = 1
log (10x² + 5) - log (1 + x² -2x) = 1
log ($\frac{10 x^{2} + 5}{ x^{2} -2x + 1 }$) = 1
10¹ = $\frac{10 x^{2} + 5}{ x^{2} -2x + 1 }$
10x² + 5 = 10 . (x² -2x + 1)
10x² + 5 = 10x² -20x + 10
10x² - 10x² + 20x = 10 - 5
20x = 5
x = $\frac{5}{20}$
x = $\frac{1}{4}$