7. (i) Find the value of \(y\) for which
$$1.01 ^ { y - 1 } = 500$$
Give your answer to 2 decimal places.
(ii) Given that
$$2 \log _ { 4 } ( 3 x + 5 ) = \log _ { 4 } ( 3 x + 8 ) + 1 , \quad x > - \frac { 5 } { 3 }$$
- show that
$$9 x ^ { 2 } + 18 x - 7 = 0$$
- Hence solve the equation
$$2 \log _ { 4 } ( 3 x + 5 ) = \log _ { 4 } ( 3 x + 8 ) + 1 , \quad x > - \frac { 5 } { 3 }$$
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