Question

Find the domain of the following function$f\left(x\right)={\log }_4\left\{{\log }_5\left({\log }_3\left(18x-x^2-77\right)\right)\right\}$

• A. $(7,11)$
• B. $(8,10)$
• C. $(-7,11)$
• D. $(-8,10)$

Answer 1

Answer: (B)

$(8,10)$

for all $log$ values to be real

${\log }_5\left({\log }_3(18x-x^2-77)\right)>0$

${\log }_3(18x-x^2-77)>1$

$18x-x^2-77>3$

$x^2-18x+80<0$

$(x-8)(x-10)<0$

$xϵ(8,10)$