Show that for any $a0$ and $a\ne 1$, it holds that \({{\log }_{{{a}^{r}}}}b=\frac{1}{r}{{\log }

Question

Show that for any $a>0$ and $a\ne 1$, it holds that ${{\log }_{{{a}^{r}}}}b=\frac{1}{r}{{\log }_{a}}b$, where $r\ne 0$. Hence, or otherwise, find the value of $\frac{4}{{{\log }_{\sqrt{x}}}\left( xyz \right)}+\frac{6}{{{\log }_{\sqrt[3]{y}}}\left( xyz \right)}+\frac{8}{{{\log }_{\sqrt[4]{z}}}\left( xyz \right)}$.

Accepted Answer

(b) $2$

Exponential and Logarithmic Functions - Higher Order Thinking Questions

Exponential and Logarithmic Functions - Higher Order Thinking Questions