Without using a calculator, find the integer value of \((5^{\lg 2}) (2^{\lg 3}) (5^{\lg 9}) (2^{\lg

Question

Without using a calculator, find the integer value of $(5^{\lg 2}) (2^{\lg 3}) (5^{\lg 9}) (2^{\lg 6})$.[3] Given that $\log_2(y^2) = 4 - \log_{0.5} x$, express $y$ in terms of $x$.[3] Solve the equation $2e^x = 3-5\sqrt{e^x}$.[4]

Accepted Answer

(i) $f'(x)=4\sin^2 2x+2\sin^2 2x\sec^2 2x$ (ii) $f'(x)>0$ for $0<x<\dfrac{\pi}{4}$, so $f$ is increasing.

2025 SST PRELIMS P1 Q2

2025 SST PRELIMS P1 Q2

Solution:

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