Question

Match the following expressions with their values.

• A. 3
• B. $\log \left(\frac{x^2}{y^3}\right)$
• C. 0.0
• D. 1

Answer 1

Case(1):
${\log }_{2}8-lo{g}_{4}64$
= ${\log }_2{2}^3-lo{g}_4{4}^3$
=$3{\log }_{2}2-3lo{g}_{4}4$
{${\log }_m{m}^n=nlo{g}_{m}m$}
and ,
{ ${\log }_{m}m=1$}
So,
$3{\log }_{2}2-3lo{g}_{4}4$
= 3-3
= 0

Case(2):

$2logx-3logy$
= $\log x^2-log{y}^3$
{${\log }_m{m}^n=nlo{g}_{m}m$}
Also
$\log \frac{m}{n}=logm-logn$
=$\log \frac{x^2}{y^3}$

Case(3):

$\frac{log64}{log4}$
= $\frac{log{4}^3}{log4}$
= $\frac{3log4}{log4}$
{${\log }_m{m}^n=nlo{g}_{m}m$}
= 3

Case(4):
${\log }_{2}16-lo{g}_{3}27$
= ${\log }_2{2}^4-lo{g}_3{3}^3$
= $4{\log }_{2}2-3lo{g}_{3}3$
{ ${\log }_{m}m=1$}
= $4-3$
= 1