<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">The variables \(x\) and \(y\) are defined such that&nbsp;\(\log_2 x - 3\log_4 y = \log_9 3\).</span></div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Give a reason why \(x\) and \(y\) must be positive numbers.</span><span class="inline-marks">[1]</span></div></li></ol></li></ol>
<ol class="i-list" start="2"><li><div class="list-item-content"><span class="list-item-text">Express \(x\) in terms of \(y\).</span><span class="inline-marks">[5]</span></div></li></ol>
<ol class="abc-list" start="2"><li><div class="list-item-content"><span class="list-item-text">Solve the equation \(5^{x+1} + 2(5^{-x}) = 11\), leaving non-exact value(s) of \(x\) in the form \(\log_a b\).</span><span class="inline-marks">[4]</span></div></li></ol>

The variables \(x\) and \(y\) are defined such that \(\log_2 x - 3\log_4 y = \log_9 3\).

Give a reason why \(x\) and \(y\) must be positive numbers.

Solve the equation \(5^{x+1} + 2(5^{-x}) = 11\), leaving non-exact value(s) of \(x\) in the form \(\log_a b\).

2025 CHS PRELIMS P2 Q3

2025 CHS PRELIMS P2 Q3