[tex]\displaystyle\bf\\\log_{a} b=z\\\\\\\log_{a^{2} }b=\log_{a} b^{\frac{1}{2} } =\frac{1}{2} \log_{a} b=\boxed{\frac{1}{2} z}[/tex]
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[tex]\displaystyle\bf\\\log_{a} b=z\\\\\\\log_{a^{2} }b=\log_{a} b^{\frac{1}{2} } =\frac{1}{2} \log_{a} b=\boxed{\frac{1}{2} z}[/tex]