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PSLE Foundation Mathematics

<ol class="abc-list"><li data-list-item-id="item-1" data-list-item-path="item-1"><div class="list-item-paragraph">Show that the solution of the equation $2^{3x+4} \times 5^{2x-1} = 16^x \times 5^{3x}$ is $\lg \frac{16}{5}$.<span class="inline-marks">[3]</span></div></li><li data-list-item-id="item-2" data-list-item-path="item-2"><div class="list-item-paragraph">Express $2\log_2 x - \log_2(x - 4) = 3$ as a quadratic equation in $x$ and explain why there are no real solutions.<span class="inline-marks">[5]</span></div></li></ol>

Solving Logarithm Equations

Solving Exponential and Power Equations Using Logarithms

2024 FMSS PRELIMS P1 Q8

Exponential and Logarithmic Functions

<p>Show that the solution of the equation $12^{x+1}=36 \times 4^{x+2}$ can be expressed as&nbsp;$1+\frac{\lg a}{\lg b}$, where <em>a </em>and <em>b </em>are integers.<span class="inline-marks">[5]</span></p>

Show that the solution of the equation $12^{x+1}=36\times4^{x+2}$ can be expressed as $1+\frac{\lg a}{\lg b}$, where $a$ and $b$ are integers.

2025 CGSS PRELIMS P2 Q2

<ol class="abc-list"><li data-list-item-id="item-1787979660079-oowocqkat" data-list-item-path="item-1787979660079-oowocqkat"><div class="list-item-paragraph"><p>Simplify $\frac{4^{x+2}-2^{2x+1}}{8^x(4^{1-x})}$ and express it in the form $a(2^{x-b})$ where $a$ and $b$ are integers.</p><span class="inline-marks">[3]</span></div></li><li data-list-item-id="item-1787979661076-m9xdoxl1k" data-list-item-path="item-1787979661076-m9xdoxl1k"><div class="list-item-paragraph"><p>Hence, solve for $x$ if $\frac{4^{x+2}-2^{2x+1}}{8^x(4^{1-x})} = 15$.</p><span class="inline-marks">[2]</span></div></li></ol>

Laws of Indices

<p>Solve the following equations</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$-2={{\log }_{7}}x-3{{\log }_{x}}7$</div><p style="text-align: right;">[3]</p></li><li><div class="list-item-paragraph">$\frac{{{2}^{2x}}}{21}=\frac{{{5}^{x}}}{6}$</div><p style="text-align: right;">[2]</p></li></ol>

2020 HYSS AM S4 P1 Q4

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