Question

log 3 value = ? for base 81
a. 1/4
b. -3
c. -4
d. None​

Answer 1

${ \boxed{ \begin{array}{cc} \bf \: log_ { 81}(3) \\ \\ \pink{ \boxed{ 81 \sf \: can \: be \: written \: as \: {3}^{4} }}\\ \\ \bf = log_{ { \green{3}}^{4} }( { \green{3}}^{1} ) \\ \\ \pink{ \boxed{ \begin{array}{cc} \sf \: we \: know \: that : \\ \\ \bf \: log_{ { \blue{x }}^{y} }( { \blue{x}}^{z} ) = \frac{z}{y} \end{array}}} \\ \\ \sf \:in \: the \:question \: \: here \: \\ \bf \: x = 3 \\ \bf \: y = 4 \\ \bf \: z = 1 \\ \\ \bf \: now \\ \\ \bf = \frac{1}{4} \\ \\ \\ \boxed{\therefore \bf \: log_{81}(3) = \frac{1}{4} }\end{array}}}$

So option a) 1/4 is the correct answer.

Answer 2

Step-by-step explanation:

We have,

$\sf log _{81}3$

$\sf \implies \bf log _{3^4}3$

$\sf \implies \bf \dfrac{1}{4}log _{3}3$

$\sf \implies \bf \dfrac{1}{4}$