SOLUTION: Please explain how to work this problem: log of(x+1), base 2 plus 2 times the log of(x-1), base 4 equals 3

Question 173045: Please explain how to work this problem:
log of(x+1), base 2 plus 2 times the log of(x-1), base 4 equals 3
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
i think i have a solution for you.
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before i go any further, your answer is:
x = 3
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i checked that out in the original formulas and it works.
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the problem:

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so i could see the problem a little easier, i let:
a = (x+1)
and
b = (x-1)
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the problem then looks like:

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i then wanted to get a common base, so i converted the logarithm with a base of 4 to a logarithm with a base of 2 using the conversion formula:

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the problem then looks like:

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since if and only if and i can show that d has to be equal to 2, then:

and the problem now looks like:

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this simplifies to:

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since the laws of logarithms state:

then:
must equal
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the problem now looks like:

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the basic laws of logarithms state:
if and only if:

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since = 8, the problem now looks like:

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if you recall from way back, i let:
a = (x+1)
b = (x-1)
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i can now substitute (x+1) for a, and (x-1) for b, and the problem now looks like:

multiplying out the factors, this becomes:

add 1 to both sides of the equation to get:

take the square root of both sides of the equation to get:

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that's your answer.
it was not a simple problem.
you needed to be able to convert bases:
you also needed to remember:
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fyi:
you could have solved by converting to as well as the way i showed you above. then you could have used the log function of the calculator to get your answer.
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