Find the value of y, if log (y + 8) + log (y - 8) = 2log 3 + 2log 5

Answer Details

To find the value of y in the equation log(y + 8) + log(y - 8) = 2log3 + 2log5, we can use some logarithmic properties.
First, let's simplify the right side of the equation. Using the property log(a) + log(b) = log(ab), we can rewrite 2log3 + 2log5 as log(3^2) + log(5^2), which becomes: log(9) + log(25)
Next, the left side of the equation can be simplified using the property log(a) + log(b) = log(ab): log((y + 8)(y - 8))
Now, our equation becomes: log((y + 8)(y - 8)) = log(9) + log(25)
To further simplify, we can apply the exponential function to both sides of the equation, which allows us to remove the logarithm function: (y + 8)(y - 8) = 9 * 25
Expanding the equation on the left side, we get: y^2 - 64 = 225
Rearranging terms, we have: y^2 = 289
Taking the square root of both sides, we get: y = ±17
Therefore, the correct answer is y = ±17.