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Question

Find the value of x if 2logx7+log7x7+3log49x7=0

A
x=43
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B
x=71/2
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C
x=74/3
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D
Either (B) or (C)
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Solution

The correct option is D Either (B) or (C)
Given
2logx7+log7x7+3log49x7=0$

2log77log7x+log77log77x+3log77log77=0

21log7x+1log77x+31log7(49x)=0

2log7x+1log77+log7x+31log749x=0

2log7x+11+log7x+32+log7x=0

Let log7x=a

2a+11+a+32+a=0

By taking LCM and cross multiplication

2(1+a)(2+a)+a(2+a)+3a(1+a)=0

2(a2+3a+2)+(2a+a2)+(3a+3a2)=0

6a2+11a+4=0

(3a+4)(2a+1)=0

3a=4

a=43

log7x=43

x=743

If 2a+1=0

2a=1

a=12

log7x=12

x=712
Hence the values of x are 712 and 743


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