Log 8(log16(log5 25))

Question

Log 8(log16(log5 25))

Answer 1

Log₈(log₁₆(log₅25))=log₈(log₁₆ 2)=log₈(1/4 *log₂ 2)= 1/3* log₂ 2⁻² = 1/3 *(-2) = -2/3

использовали, что log₅25 = log₅ 5² = 2
                               log₁₆ 2 = log₂⁴ 2 = 1/4 log₂ 2 = 1/4 *1 = 1/4
                               log₈ (1/4) = log₂³(1/2)²=1/3 *log₂(2)⁻² = 1/3*(-2) =-2/3