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Solving for x in logarithm problem

The equation (attached as image) has

(a)one irrational solution

(b)no prime solution

(c)two real solutions

(d)one integral solution

i would like to get help on how to find the possible values of x

i solved the equation by applying the base changing property and then doing

L.C.M of both equations but after that i am unable to solve further?

Any help will be highly appreciated.

Re: Solving for x in logarithm problem

Show what you tried so far.

What results?

I suggest: Do change of base with base of 2 .

Re: Solving for x in logarithm problem

2/log2(x) + 6/ (log2(x)+1)=3

i got this result

after that what should i do

Re: Solving for x in logarithm problem

Re: Solving for x in logarithm problem

Re: Solving for x in logarithm problem

thank you very much i got it