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Question

Solve for x :
log3/4log8(x2+7)+log1/2log1/4(x2+7)−1=−2

A
x=3
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B
x=5
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C
x=3
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D
x=6
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Solution

The correct options are
A x=3
C x=3
log3/4[13log2(x2+7)]+log1/2[12log2(x2+7)]=2

By logbpan=nplogba

log22(x2+7)1=11log2(x2+7)

Let log2(x2+7)=tx2+7=2t

log3/4(13t)+log1/2(12t)=2

log(t/3)log(3/4)+log1/212+log1/2t=2

logtlog3log3log4+log1/212+log1/2t=2

logtlog32log2log3log32log2+1logtlog2=2

logt[log2log3+2log2](log32log2)log2

=3+log3log32log2

logt[3log2log3](log32log2)log2=6log22log3log32log2

logt=2log2=log22=log4

t=4x2+7=2t=24=16

or x2=9x=±3

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