Moderate -0.3 Part (i) requires standard manipulation of exponential equations using logarithms and expressing in a specific form, while part (ii) involves routine application of logarithm laws. Both are textbook-style exercises with clear methods, though part (i) requires careful algebraic manipulation to reach the required form. Slightly easier than average due to being straightforward applications of standard techniques.
8. (i) Find the exact solution of the equation
$$8 ^ { 2 x + 1 } = 6$$
giving your answer in the form \(a + b \log _ { 2 } 3\), where \(a\) and \(b\) are constants to be found.
(ii) Using the laws of logarithms, solve
$$\log _ { 5 } ( 7 - 2 y ) = 2 \log _ { 5 } ( y + 1 ) - 1$$
8. (i) Find the exact solution of the equation
$$8 ^ { 2 x + 1 } = 6$$
giving your answer in the form $a + b \log _ { 2 } 3$, where $a$ and $b$ are constants to be found.\\
(ii) Using the laws of logarithms, solve
$$\log _ { 5 } ( 7 - 2 y ) = 2 \log _ { 5 } ( y + 1 ) - 1$$
\hfill \mbox{\textit{Edexcel P2 2019 Q8 [9]}}