I'm having a hard time finding the value of $a$ in this problem. My teacher was trying to explain to me the process in which to get it but I did not understand him.
2026-05-15 21:58:40.1778882320
If log8n=1/2p, log22n=q, and q-p=4, find n
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hint:$$(\log_4x)^2= (\log_42\cdot \log_2x)^2=\dfrac{1}{4}(\log_2x)^2\Rightarrow \log_2x(4\log_ax-\log_2x)=0\Rightarrow \log_2x=0 \text{ or } 4\log_ax=\log_2x$$. The former equation gives: $x = 1$, the latter leads to: $4\log_a2\cdot \log_2x= \log_2x \Rightarrow \log_2x(4\log_a2-1)=0$. Can you continue?