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Question

If (3x)log3=(4y)log4 and 4logx=3logy, then the value of x will be

A
14
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B
13
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C
3
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D
4
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Solution

The correct option is B 13
Taking log on both sides of given equations,
log3log(3x)=log4log(4y)
log3(log3+logx)=log4(log4+logy)[log(ab)=loga+logb] (i)
And, logxlog4=logylog3
logx(log4)=(logy)log3 (ii)
From (i)
(log4)2(log3)2=log3logxlog4logy (iii)
From (ii)
logxlog3=logylog4=λ(say) (iv)
From (iv) and (iii)
(log4)2(log3)2=[(log3)2(log4)2]λ
λ=1
logx=log3=log13
logy=log4=log14
x=13,y=14

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