Odpowiedź:
6.
a)
log₂1 + 1/2log₂16 = 0 + log₂16¹⁾² = log₂√16 = log₂4 = 2
b)
log₃27 - log₄1 = 3 - 0 = 3
c)
log₄4 - log₄64 = 1 - 3 = - 2
d)
log₅125 - log₅1/5 = 3 - (- 1) = 3 + 1 = 4
7.
a) 4³⁾² = √4³ = √64 = 8
b) 27²⁾³ = (∛27)² = 3³ = 9
c) 8⁴⁾³ = (∛8)⁴ = 2⁴ = 16
d) 32³⁾⁵ = (⁵√32)³ = 2³ = 8
8.
a) (3/4)⁻⁵ : (3/4)⁻³ = (3/4)⁻⁵⁺³ = (3/4)⁻² = (4/3)² = 16/9 = 1 7/9
b) (3/8)⁷ : (3/8)⁸ = (3/8)⁷⁻⁸ = (3/8)⁻¹ = 8/3 = 2 2/3
c) (3⁶)⁻² * 3¹⁰ = 3⁻¹² * 3¹⁰ = 3⁻¹²⁺¹⁰ = 3⁻² = (1/3)² = 1/9
9.
a ) √125 = √(25 * 5) = 5√5 - liczba niewymierna
b) √286 - liczba niewymierna
