If \log_4 x^2(x-a)^2-\log_2(x-1)=1, then the value of x will be:

Logarithms Practice Test 2

Question : 12 of 39

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\log_4 x^2(x-a)^2-\log_2(x-1)=1,

then the value of x will be:

Solution:

\log_4 x^2(x-a)^2-\log_2(x-1)=1

⇒\log_{2^2}[x(x-1)]^2-\log_2 (x-1)=1

⇒2/2\log_2{x(x-1)}-\log_2(x-1)=1

⇒\log_2{x(x-1)}/{x-1}=1

⇒\log_2 x=1

∴x=2^1=2

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