Question

Find the value of ${}^{\prime }{x}^{\prime }$ if $3\log 2+\frac{1}{3}\log 27-\log 4=\log x$

Answer 1

LHS

$=>3log\left(2\right)+\frac{1}{3}log\left(27\right)-log\left(4\right)$

for $\frac{1}{3}log27$

$=>\frac{1}{3}log{3}^3$ $[log{a}^b=bloga$]

$=>3\times \frac{1}{3}log3$

$=>log3---------------\left(i\right)$

for $log4$

$=>log{2}^2$ $[log{a}^b=bloga$]

$=>2log2----------------\left(ii\right)$

now finally,

from $\left(i\right)$ and $\left(ii\right)$ we get,

$=>3log\left(2\right)+log\left(3\right)-2log\left(2\right)$

add similar elements

$=>3log\left(2\right)-2log\left(2\right)$

$=>log\left(2\right)$

$=>log\left(2\right)+log\left(3\right)$

$=>log(2\times 3)$

$=>log\left(6\right)$ ans