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4.5.3 Indices and Logarithms, Short Questions (Question 8 – 10)


Question 8
Solve the equation, log9(x2)=log32

Solution:
log9(x2)=log32logab=logcblogcalog3(x2)log39=log32log3(x2)2=log32log3(x2)=2log32log3(x2)=log322x2=4x=6



Question 9
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+2x8=0(x+4)(x2)=0x=4 (not accepted)x=2



Question 10
Solve the equation, log4x=32log23

Solution:
log4x=32log23log2xlog24=32log23log2x2=32log23log2x=2×32log23log2x=3log23log2x=log233x=27


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