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JAMB Mathematics 2023 Paper

Question : 27

Total: 80

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

Solution:

Concept:

Use the laws of logarithms to combine both sides, then equate the arguments.

Explanation:

Start with the given equation:

\log(y+8)+\log(y-8)=2\log3+2\log5.

Combine the left side using

\log a+\log b=\log(ab)

\log[(y+8)(y-8)]=\log(y^2-64).

Simplify the right side by writing the coefficients as powers:

2\log3+2\log5=\log3^2+\log5^2=\log9+\log25=\log225.

Now the equation becomes:

\log(y^2-64)=\log225.

Since the logs have the same base, set the arguments equal:

y^2-64=225.

Solve for

y

y^2=225+64=289,

y=\pm\sqrt{289}=\pm17.

Answer:

y=\pm17

(Option C).

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