csat-suneung 2006 Q24

csat-suneung · South-Korea · csat__math-humanities 4 marks Laws of Logarithms Optimize a Logarithmic Expression
For the function with domain $\{ x \mid 1 \leqq x \leqq 81 \}$, $$y = \left( \log _ { 3 } x \right) \left( \log _ { \frac { 1 } { 3 } } x \right) + 2 \log _ { 3 } x + 10$$ Let $M$ be the maximum value and $m$ be the minimum value. Find the value of $M + m$. [4 points]
For the function with domain $\{ x \mid 1 \leqq x \leqq 81 \}$,
$$y = \left( \log _ { 3 } x \right) \left( \log _ { \frac { 1 } { 3 } } x \right) + 2 \log _ { 3 } x + 10$$
Let $M$ be the maximum value and $m$ be the minimum value. Find the value of $M + m$. [4 points]