SOLUTION: 1. Prove that. (I) log3. Log2. Log√3 81=1 (ii) Logax X logby = Logbx X logay (iii) log2. Log2. Log2 16=1

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 1. Prove that. (I) log3. Log2. Log√3 81=1 (ii) Logax X logby = Logbx X logay (iii) log2. Log2. Log2 16=1       Log On


   

Question 991815: 1. Prove that. (I) log3. Log2. Log√3 81=1
(ii) Logax X logby = Logbx X logay
(iii) log2. Log2. Log2 16=1
Answer by ikleyn(52814) About Me  (Show Source):
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(iii) log2. Log2. Log2 16=1
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The statement is: log%282%2C+%28log%282%2C+%28log%282%2C16%29%29%29%29%29 = 1.

Proof: log%282%2C+%28log%282%2C+%28log%282%2C16%29%29%29%29%29 = log%282%2C+%28log%282%2C+4%29%29%29%29         (since log%282%2C16%29 = 4)

                                            = log%282%2C+2%29                   (since log%282%2C4%29 = 2)

                                            = 1.