**5.5 Indeks dan Logaritma, SPM Praktis (Soalan Pendek)**

**Soalan 12**

Selesaikan persamaan, ${\mathrm{log}}_{2}5\sqrt{x}+{\mathrm{log}}_{4}16x=6$

*Penyelesaian:***Soalan 13**

Diberi bahawa 2 log

_{2}(*x*–*y*) = 3 + log_{2}*x*+ log_{2}*y*. Buktikan*x*^{2}+*y*^{2}– 10*xy*= 0.

*Penyelesaian:*2 log

_{2}(*x*–*y*) = 3 + log_{2}*x*+ log_{2}*y*log

_{2}(*x*–*y*)^{2}= log_{2}8 + log_{2}*x*+ log_{2}*y*log

_{2}(*x*–*y*)^{2}= log_{2}8*xy*(

*x*–*y*)^{2}= 8*xy**x*

^{2}– 2

*xy*+

*y*

^{2}= 8

*xy*

*x*

^{2}**+**

*y*^{2}– 10*xy*= 0 (terbukti)**Soalan 14**

Diberi bahawa 2 log

_{2}(*x*+*y*) = 3 + log_{2}*x*+ log_{2}*y*. Buktikan*x*^{2}+*y*^{2}= 6*xy*.

*Penyelesaian:*2 log

_{2}(*x*+*y*) = 3 + log_{2}*x*+ log_{2}*y*log

_{2}(*x*+*y*)^{2}= log_{2}8 + log_{2}*x*+ log_{2}*y*log

_{2}(*x*+*y*)^{2}= log_{2}8*xy*(

*x*+*y*)^{2}= 8*xy**x*

^{2}+ 2

*xy*+

*y*

^{2}= 8

*xy*

*x*

^{2}**+**

*y*^{2}= 6*xy*(terbukti)