Question 5
Solve the equation,
log9(x−2)=log32
Solution:
log9(x−2)=log32logab=logcblogca⇒log3(x−2)log39=log32log3(x−2)2=log32log3(x−2)=2log32log3(x−2)=log322x−2=4x=6
Question 6
Solve the equation,
log9(2x+12)=log3(x+2)
Solution:
log9(2x+12)=log3(x+2)log3(2x+12)log39=log3(x+2)log3(2x+12)=2log3(x+2)log3(2x+12)=log3(x+2)22x+12=x2+4x+4x2+2x−8=0(x+4)(x−2)=0x=−4 (not accepted)x=2
Question 7
Solve the equation,
log4x=32log23
Solution:
Question 8
Solve the equation,
2log52=log2(2−x)
Solution:
2log52=log2(2−x)2=log52.log2(2−x)2=1log25.log2(2−x)2log25=log2(2−x)log252=log2(2−x)25=2−xx=−23