SOLUTION: How do I go about this question? Find the value of x for: log2(x2 + 4x + 3) � log 2(x2 + x) = 4

Question 254819: How do I go about this question?
Find the value of x for:
log2(x2 + 4x + 3) � log 2(x2 + x) = 4
Found 2 solutions by palanisamy, Theo:
Answer by palanisamy(496) (Show Source): You can put this solution on YOUR website!
Given, log2(x2 + 4x + 3) � log 2(x2 + x) = 4
log2[(x^2+4x+3)/(x^2+x)] = 4
Taking anti-log, we get
[(x^2+4x+3)/(x^2+x)] =2^4
x^2+4x+3 = 16(x^2+x)
x^2+4x+3 = 16x^2+16x
0 = 15x^2+12x-3
Dividing by 3, we get
5x^2+4x-1 = 0
(5x-1)(x+1)=0
x = -1,1/5

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
problem is:

since , then the reverse is also true, i.e.:

applying this rule of logarithms makes your equation become:

since if and only if , applying this rule makes your equation become:

multiply both sides of this equation by and you get:

multiply the factors out and you get:

subtract from both sides of this equation and combine like terms to get:

factor this equation to get:

solve for x to get:

or

confirm by substituting in original equation of:

to confirm using your calculator, you need to convert the base of the logarithm from 2 to 10 or e.

I used 10 because it is the LOG function of my calculator.

the conversion formula says:

if we let a = base of 2 and we let c = base of 10, this formula becomes:

your formula of becomes:

substituting x = (1/5) into this equation, we get:

this becomes:

which becomes:

confirming that x = (1/5) is good.

when x = -1, confirmation was not successful because:

original equation is:

substitute -1 for x to get:

this becomes:

since you can't take log of 0 to any base, x = -1 is not a valid answer.

graph of your original equation looks like this:

the answer to your problem is:

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