Question

The value of the expression:
$log{18}^{3/2}+3log(2\times 2)-2log(3\times 2)is:$

• A. $log96\sqrt{2}$
• B. $log45\sqrt{3}$
• C. $0$
• D. $1$

Answer 1

The correct option is A $log96\sqrt{2}$

$\log {18}^{3/2}+3\log (2\times 2)-2\log (3\times 2)$

$=\frac{3}{2}\log 18+\log 4^3-\log 6^2$

$=\frac{3}{2}\log 18+\log \frac{64}{36}$

$=\frac{3}{2}\log 18+\log \frac{16}{9}$

$=\log \left[\right(9\times 2{)}^{3/2}\times \left(\frac{16}{9}\right)]$

$=\log \left[\right(9{)}^{1/2}(2{)}^{3/2}\times (2{)}^4]$

$=\log [3\cdot 2^{11/2}]$

$=\log (3\cdot 32\cdot 2^{1/2})$

$=\log \left(96\sqrt{2}\right)$