Let log_-1/381 = x
? 81 = (-1/3)^x
? 3⁴ = (-1/3)^x = 3^-x
? x = -4

If log₁₀{log₁₀[log₁₀(log₁₀N)]} = 0
? log₁₀{log₁₀(log₁₀N)} = 1
? log₁₀(log₁₀N) = 10
? log₁₀^N = 10¹⁰
? N = 10¹⁰¹⁰

Exp. = 25 log₅4 = 5² log₅4
= 5 log₅ 4²
= 16

Exp. = log₁₀ 10^-6 = -6

Exp. = log₁₀ 10^-5 = -5

log₆ log₅15625 = log₆ log₅(5)⁶
= log₆6(log₅5) = 1

? log₁₀⁴x = -1/4
? x = (10⁴)^-1/4
= 1/10

? log_x(16/25) = -1/2
? 16/25 = (x)^-1/2 = 1/x^1/2
? x = 625/256

log₂(1/64) = log₂1 - log₂ 2⁶
= 0 - 6 = -6

? log_a3 = 1/3
? 3 = (a)^1/3
? a = 27