Find the value of y if log y 8 log y - 8 2log 3... - JAMB Mathematics 2023 Question

Let's solve the given logarithmic equation:

\[ \log(y + 8) + \log(y - 8) = 2\log 3 + 2\log 5 \]

We can use logarithmic properties to simplify the equation. The sum of logarithms is equal to the logarithm of their product:

\[ \log((y + 8)(y - 8)) = \log(3^2 \cdot 5^2) \]

Now, we can set the arguments equal to each other:

\[ (y + 8)(y - 8) = 3^2 \cdot 5^2 \]

Expand and simplify the equation:

\[ y^2 - 64 = 9 \cdot 25 \]

\[ y^2 = 9 \cdot 25 + 64 \]

\[ y^2 = 225 + 64 \]

\[ y^2 = 289 \]

Now, take the square root of both sides:

\[ y = \pm \sqrt{289} \]

So, \( y = \pm 17 \).

Therefore, the correct answer is \( y = \pm 17 \)