Question

log base5. 25-Log5 (x mas 100) igual -1

Answer 1

log₅ 25 - log ₅ (x+100) = -1
2 - log₅ (x+100)= -1
- log₅ (x+100) = -1-2 = -3
 log₅ (x+100) = 3        *aplicamos definición de log:

5³ = x+100
125 = x+100
x = 125-100 = 25
x= 25

Answer 2

Aplicando propiedades y definición de logaritmos

$log(5)25- log(5)(x + 100) = - 1 \\ \\ log(5)( \frac{25}{x + 100}) = - 1 \\ \\ \frac{25}{x+100} = 5^{-1} \\ \\ \frac{25}{x+100} = \frac{1}{5} \\ \\ 25.5=x+100 \\ \\ 125=x+ 100 \\ \\ x=125-100 \\ \\ x=25$