Question

log[2](x-3)-log[2](2x+1)=-log[2]4

Answer 1

Teniendo en cuenta que:

• logb A  - logb B = log(A/B)
• logb A^n = n logb A
• Si logb A = logb B , entonces: A = B

Resolvemos:

$log_2(x-3) - log_2(2x+1) = -log_2(4) \ \ log_2(\frac{x-3}{2x+1}) = log_2 (4^{-1})$

$\frac{x-3}{2x+1} = \frac{1}{4} \ \ 4x - 12 = 2x+1 \ \ 4x - 2x = 12 + 1 \ \ 2x = 13 \ \ \boxed{x = 13/2}$

Saludos!