¿Porque nosotros tenemos que hacer eso si te lo dieron a vos?

= Log(100) + Log[5](1/25) - Log[3](1/27) → recall: Log[a](x) = Ln(x)/Ln(a) where a is the base

= Log(100) + [Ln(1/25) / Ln(5)] - [Ln(1/27) / Ln(3)] → recall: Log(x) = Ln(x)/Ln(10) where a is the base

= [Ln(100) / Ln(10)] + [Ln(1/25) / Ln(5)] - [Ln(1/27) / Ln(3)] → recall: Ln(1/x) = - Ln(x)

= [Ln(100) / Ln(10)] + [- Ln(25) / Ln(5)] - [- Ln(27) / Ln(3)]

= [Ln(100) / Ln(10)] - [Ln(25) / Ln(5)] + [Ln(27) / Ln(3)]

= [Ln(10^2) / Ln(10)] - [Ln(5^2) / Ln(5)] + [Ln(3^3) / Ln(3)] → recall: Ln(x^a) = a.Ln(x)

= [2.Ln(10) / Ln(10)] - [2.Ln(5) / Ln(5)] + [3.Ln(3) / Ln(3)]

= [2] - [2] + [3]

= 3

como

10^2 = 100

log(100) = 2

como

5^(-2) = 1/5^2 = 1/25

log_5(1/25) = -2

como

3^(-3) = 1/3^3 = 1/27

log_3(1/27) = -3

Supongo

log(100) + log_5(1/25) - log_3(1/27) = 2 - 2 - (-3) = 3

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