Explanation:
log¹⁰ a^{\(\frac{1}{3}\)} + \(\frac{1}{4}\)log₁₀ a - \(\frac{1}{12}\)log₁₀a⁷ = log¹⁰ a^{\(\frac{1}{3}\)} + log¹⁰\(\frac{1}{4}\) - log₁₀ a^{\(\frac{7}{12}\)}
= log₁₀ a^{\(\frac{7}{12}\)} - log₁₀ a^{\(\frac{7}{12}\)}
= log₁₀ 1 = 0