Determine the values of $$ x $$ and $$ y $$, in the equation: $$ \frac{x-1}{3+i}+\frac{y-1}{3-i}=i $$. Solve the following equations: i) $$ 2^{2 x+1}=3^{2 x-5} \quad $$ ii) $$ \log _{2} x-\log _{2} y=2 $$ $$ \log _{2}(x-2 y)=3 $$ In a senior secondary school, 80 students play hockey or football. The number that plays football is 5 more than twice the number that play hockey. If 15 students play both games and every student in the schoo plays at least one game, find the number of students that play football.

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Barker Higgins · Accepted Answer

**Solutions:** 1. **Complex Equation:** $$ x = -4 \quad \text{and} \quad y = 6 $$ 2. **Exponential and Logarithmic Equations:** - **i)** $$ x = \dfrac{5 \ln 3 + \ln 2}{2 (\ln 3 - \ln 2)} $$ - **ii)** $$ x = 16 $$ and $$ y = 4 $$ 3. **Sports Problem:** $$ 65 \text{ students play football} $$

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