Use the substitution $u = 7^x$, solve the equation $7^{2x+2} - 4(7^{x+1}) - 5 = 0$ and show that

Question

Use the substitution $u = 7^x$, solve the equation $7^{2x+2} - 4(7^{x+1}) - 5 = 0$ and show that the solution may be written in the form $\log_{a} b - 1$ where $a$ and $b$ are integers to be determined.[4] Solve the equation $\log_{3} (2x - 1) - \log_{9} (x^2 + 2) = \log_{25} 5$.[5]

Accepted Answer

(a) $x=\log_7 5-1$, $a=7,b=5$. (b) $x=5$.

2025 SCGS PRELIMS P2 Q2

2025 SCGS PRELIMS P2 Q2

Solution:

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