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 $y=\pm 17$