The value of displaystyle lim x arrow 3( log a (x-3/√x+6-3)) is

Question

The value of displaystyle lim x arrow 3( log a (x-3/√x+6-3)) is (A)  log a 6 (B)  log a 3 (C)  log a 2 (D) None of these

Tardigrade Admin · Accepted Answer

displaystyle lim x arrow 3[ log a (x-3/√x+6-3)] = displaystyle lim x arrow 3[ log a ((x-3)(√x+6+3)/(x-3))] = displaystyle lim x arrow 3 log a(√x+6+3)= log a 6 displaystyle lim x arrow a (xn-an/x-a)=n an-1 where n ∈ Q, the set of rational numbers.

Q. The value of $x \to 3 lim (lo g_{a} \frac{x - 3}{x + 6 - 3})$ is

$lo g_{a} 6$

$lo g_{a} 3$

$lo g_{a} 2$

None of these

$x \to 3 lim [lo g_{a} \frac{x - 3}{x + 6 - 3}]$
$= x \to 3 lim [lo g_{a} \frac{( x - 3 ) ( x + 6 + 3 )}{( x - 3 )}]$
$= x \to 3 lim lo g_{a} (x + 6 + 3) = lo g_{a} 6$
$x \to a lim \frac{x ^{n} - a ^{n}}{x - a} = n a^{n - 1}$
where $n \in Q$ , the set of rational numbers.

Q. The value of x→3lim​(loga​x+6​−3x−3​) is

loga​6

loga​3

loga​2