1)log₃ [tex]\frac{1}{2}[/tex] + log₃6=
2) 81^1/4 - 3√3 × 3^1/2=

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1) To solve log equations, you can combine the logs by using the property that logₐ(m) + logₐ(n) = logₐ(mn). So,
log₃ [tex]\frac{1}{2}[/tex] + log₃6 = log₃ [tex]\frac{1}{2}[/tex] × 6
= log₃3 = 1

2) Using the properties of exponents and radicals,
81^1/4 = √(√(81)) = √(9) = 3
3√3 = 3^(1/2) × 3 = 3√3 = 3
So,
81^1/4 - 3√3 × 3^1/2= 3 - 3 × 3
= 3 - 9
= -6.