Logarithms Are Tricky

Algebra Level 2

55=3125log53125=545=1024log41024=535=243log3243=525=32log232=5\large{ \begin{array}{lll} &5^5 = 3125 &\Rightarrow &\log_5 3125 = 5 \\ &4^5 = 1024 &\Rightarrow &\log_4 1024 = 5 \\ &3^5 = 243 &\Rightarrow &\log_3 243 = 5 \\ &2^5 = 32 &\Rightarrow &\log_2 32 = 5 \end{array}}

The above mathematical working are all correct.
Given that 15=1 1^5 = 1, is it true that log11=5\log_1 1 = 5 ?

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