Question

Calcule o valor da soma S
a) S = log4 (log2 16) - log2 (log3 81)
b) S = log√2 8 - log10 0,01 + log2 √8

Answer 1

a) S =  log₄ (log₂ 16) - log₂ (log₃ 81) => S = log₄ (log₂ 2⁴) - log₂ (log₃ 3⁴) => S = log₄ 4 - log₂ 4 => S = 1 - log₂ 2² => S = 1 - 2 => S = -1

b) S = log$_{\sqrt{2} }$ 8 - log₁₀ 0,01 + log₂ √8 => S = log$_{2^{\frac{1}{2} } }$ 2³ - log₁₀ 10⁻² + log₂ √2³ => S = 6 - (-2) + log₂ $2^{\frac{3}{2} }$ => S = 6 + 2 + $\frac{3}{2}$ => S = 8 + $\frac{3}{2}$ => S = $\frac{16 + 3}{2}$ => S = $\frac{19}{2}$