Question

Find the domains of definition of the following functions.
$f\left(x\right)=lo{g}_{2x-5}(x^2-3x-10).$

Answer 1

base must be positive and not equal to 1

therefore $2x-5>0$,x not equal to 3

similarly $x^2-3x-10$>0

for first case solution is x belongs to $(5/2,\infty )-3$

for second case solution is $(-\infty ,-2)\cup (5,\infty )$

therefore the domain is $(5,\infty )$