Logarithm questions

user November 8, 2023

(56) If $\log_{a}(x) = p$ and $\log_{b}(x) = q$ , what is $\log_{ab}(x)$ ?

(a) $p + q$
(b) $p \cdot q$
(c) $p – q$
(d) $q – p$

Correct Answer: (a) $p + q$
$encoding="application/x-tex">\log_{ab}(x) = \frac{\log_{a}(x)}{\log_{a}(b)} + \frac{\log_{b}(x)}{\log_{b}(a)} = p + q</annotation></semantics></math>$

(57) If $\log_{4}(16) = x$ , what is the value of $x$ ?

(a) 2
(b) 3
(c) 4
(d) 1

Correct Answer: (a) 2
$encoding="application/x-tex">\log_{4}(16) = 2</annotation></semantics></math>$

(58) If $\log_{3}(81) = x$ , what is the value of $x$ ?

(a) 4
(b) 3
(c) 2
(d) 1

Correct Answer: (a) 4
$encoding="application/x-tex">\log_{3}(81) = 4</annotation></semantics></math>$

(59) If $\log_{a}(x) = p$ and $\log_{b}(x) = q$ , what is $\log_{ab}(x)$ ?

(a) $p + q$
(b) $p \cdot q$
(c) $p – q$
(d) $q – p$

Correct Answer: (a) $p + q$
$encoding="application/x-tex">\log_{ab}(x) = \frac{\log_{a}(x)}{\log_{a}(b)} + \frac{\log_{b}(x)}{\log_{b}(a)} = p + q</annotation></semantics></math>$