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Question

The number of solutions of log4x-1=log2x-3


A

3

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B

1

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C

2

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D

0

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Solution

The correct option is B

1


Explanation for correct option

Given, log4x-1=log2x-3

log4x-1=log412x-3log4x-1=2log4x-3log4x-1=log4x-32x-1=x-32x-1=x2-6x+9x2-7x+10=0x2-5x-2x+10=0xx-5-2x-5=0x-5x-2=0x=2,5

At x=2,logx-3 is undefined.

At, x=5,logx-3 will be log2,

x=5

So, one solution exist

Hence, the correct option is OptionB


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