Logarithms Are Tricky

Algebra Level 2

\[\large{ \begin{array}{lll} &5^5 = 3125 &\Rightarrow &\log_5 3125 = 5 \\ &4^5 = 1024 &\Rightarrow &\log_4 1024 = 5 \\ &3^5 = 243 &\Rightarrow &\log_3 243 = 5 \\ &2^5 = 32 &\Rightarrow &\log_2 32 = 5 \end{array}} \]

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