0\; ,\; a\ne 1\; ,\; x>0\\\\\\log\, _{\sqrt[7]{11}}\, 11=\frac{1}{1/7}\cdot \underbrace {log\, _{11}\, 11}_{1}=7\cdot 1=7" alt="\boxed {log_{a^{k}}x=\frac{1}{k}\cdot log_{a}x\; \; ,\; \; log_{a}a=1}\; \; ,\; \; a>0\; ,\; a\ne 1\; ,\; x>0\\\\\\log\, _{\sqrt[7]{11}}\, 11=\frac{1}{1/7}\cdot \underbrace {log\, _{11}\, 11}_{1}=7\cdot 1=7" align="absmiddle" class="latex-formula">