Calcula en cada caso el termino que falta?

Aplicaremos la propiedad del logaritmo que establece :

<img src="https://tex.z-dn.net/?f=log_%7Ba%7D%20b%20%3D%20%20%5Cfrac%7Blnb%7D%7Blna%7D%20" />

a)<img src="https://tex.z-dn.net/?f=log_%7B%20%5Csqrt%7B25%7D%20%7D%20125%20%3D%20x" />

ln(125) / ln(√5) = x

3 = x

b)<img src="https://tex.z-dn.net/?f=log_%7Bx%7D81%3D-4" />

ln(81) / lnx = - 4

ln(81) / - 4 = ln(x) - 1.

099 = ln(x) (aplicamos función exponencial)

x = <img src="https://tex.z-dn.net/?f=e%5E%7B-1.0.99%7D%20" />

x = 0.

333

c)<img src="https://tex.z-dn.net/?f=log_%7B%20%5Csqrt%7B2%7D%20%7D0.25%20%3D%20x%20" />

ln(0.

25) / ln(√2) = x

x = - 4

d)<img src="https://tex.z-dn.net/?f=log_%7B2%7D%20%20x%5E%7B3%7D%3D6%20" />

ln(x³) / ln(2) = 6

1.

442ln(x³) = 6

ln(x³) = 4.

16 (aplicamos la función exponencial)

x³ = <img src="https://tex.z-dn.net/?f=e%5E%7B4.16%7D%20" />

x³ = 64.

128

x = <img src="https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B64.128%7D" />

x = 4.