Question

log(x + 5) - 1/2 log(4x²) = 0

Answer 1

$log(x+5)- \frac{1}2}*log(4x^2)=0 \\\\log(x+5)- \frac{1}2}*log(2^2x^2)= 0\\\\log(x+5)- \frac{1}2}*log((2x)^2)= 0\\\\log(x+5)- \frac{1}2}*2*log(2x)=0 \\\\log(x+5)-log(2x) =0\\\\log(x+5)=log(2x)\\\\x+5=2x\\\\5=2x-x\\\\\boxed{5=x}$

Answer 2

log (x + 5) - 1/2 . log (4.x²) = 0
log (x + 5) - 1/2 . (log 4 + log x²) = 0
log (x + 5) - 1/2 . (log 4 + 2.log x) = 0
log (x + 5) - 1/2 . log 4 + log x = 0
log (x + 5) - log √4 + log x = 0
log (x + 5) - log 2 + log x = 0
log (x + 5) / 2 + log x = 0
log x.(x + 5) / 2 = 0
x.(x + 5) / 2 = 10°
(x² + 5.x) / 2 = 1
x² + 5.x = 2
x² + 5.x - 2 = 0

Δ = 5² - 4.1.(-2) = 25 + 8 = 33

x' = -5 + √33 = -5 + 5,744 = 0,744
x'' = -5 - √33 = -5 - 5,744 = -10,744