SOLUTION: the problem is: log base of 2 times (x+20) minus log base of 2 times (x+2) is equal to log base of 2 x. this is how far i have gotten: log base of 2 times (x+20/x+2) is equal

Question 177517This question is from textbook Precalculus graphs and models
: the problem is:
log base of 2 times (x+20) minus log base of 2 times (x+2) is equal to log base of 2 x.
this is how far i have gotten:
log base of 2 times (x+20/x+2) is equal to log base of 2 x This question is from textbook Precalculus graphs and models

Found 2 solutions by stanbon, Electrified_Levi:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
log base of 2 times (x+20) minus log base of 2 times (x+2) is equal to log base of 2 x
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log(base2)(x+20) - log(base2)(x+2) = log(base2)x
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It's all base 2 so just keep that in mind:
log(x+20) - log(x+2) = log2
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since logA - logB = log(A/B) you get:
log[(x+20)/(x+2)] = log2
Taking the inverse log you get:
(x+20)/(x+2) = 2
x+20 = 2(x+2)
x + 20 = 2x + 4
x = 16
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Cheers,
Stan H.

Answer by Electrified_Levi(103) (Show Source): You can put this solution on YOUR website!
Hi, Hope I can help
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You are correct
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If you subtract the same number log by the log, it is the same as one complete log as a fraction/division
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This is where you got stuck, from here we can use a really easy method called "undo"
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Since this equation has the same base/log (2) on both sides, we can just "undo" , get rid of, erase, cross out the logs
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=
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Now just solve for "x"
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, we will multiply each side by (x+2) to get rid of the fraction
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= = = = , we will use distribution on the right side
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= = =
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We will now move "x + 20" to the right side
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= =
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or , this is a quadratic equation, we can solve this equation by factoring
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To find the factors, we have to have multiples of "-20", and the multiples have to add up to the middle term, or "1"
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Factors of (-20)
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(2,(-10)) No
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(4,(-5)) No
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(5,(-4)) Yes, (these factors add up to "1")
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Since there was only , that means there are only "x's"
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(x)(x), you would then put the factors inside
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(x+5)(x-4) are the factors, you can check using the foil method, but I already checked
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, now we can solve for "x", you can find "x" by putting each factor equal to zero
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, now move "5" to the right side
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=
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, now move (-4) to the right side
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=
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These are your answers, but, you have to make sure and plug your answers into the original equation, and make sure that the numbers don't make a negative, because you can't take the log of a negative number
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(-5), , we don't have to go any further, since we already found a negative, (-5) will not work
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(4), = , there are no negatives, "4" will work
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Here is the graph of the equation
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Remember though that you cannot take the log of a negative, your only answer is
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Hope I helped, Levi
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