Question

If $\log (x+5)+\log (x-5)=4\log 2+2\log 3$, then the value of $x$ is equal to

• A. $11$
• B. $16$
• C. $10$
• D. $13$

Answer 1

Answer: (D)

$13$

$x-5>0andx+5>0$

$\log (x+5)+\log (x-5)=4\log 2+2\log 3$

$\log (x+5)+\log (x-5)=\log 2^4+\log 3^2$

$\log (x+5)(x-5)=\log \left(2^4{\times 3}^2\right)$

$\log (x^2-25)=\log (2^4\times 3^2)$

Removing $\log$, we get

$x^2-25=16\times 9$

$\therefore x^2=144+25=169\therefore x=13$