Show that the solution of the equation $2^{3x+4} \times 5^{2x-1} = 16^x \times 5^{3x}$ is \(\lg \f

Question

Show that the solution of the equation $2^{3x+4} \times 5^{2x-1} = 16^x \times 5^{3x}$ is $\lg \frac{16}{5}$.[3] Express $2\log_2 x - \log_2(x - 4) = 3$ as a quadratic equation in $x$ and explain why there are no real solutions.[5]

Accepted Answer

(a) $x=\lg\left(\frac{16}{5}\right)$ (b) $x^2-8x+32=0$, with no real solutions

2024 FMSS PRELIMS P1 Q8

2024 FMSS PRELIMS P1 Q8

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