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Question 1105066: what are the reasons for these steps that go in the boxes correctly to this problem log2(5)+log2(x+2)-log2(x+1)=log2(7)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the log rules that apply are:
log(x) + log(y) = log(x * y)
log(x) - log(y) = log(x / y)
if log(x) = log(y), then x = y
when you solve this problem, you use these properties of logs.
start with log2(5)+log2(x+2)-log2(x+1)=log2(7)
since log2(5)+log2(x+2) = log2(5*(x+2)), then your equation becomes:
log2(5*(x+2)) - log2(x+1) = log2(7)
since log2(5*(x+2)) - log2(x+1) = log2(5*(x+2)/(x+1)), then your equation becomes:
log2(5*(x+2)/(x+1)) = log2(7)
this is true if and only if 5*(x+2)/(x+1) = 7
multiply both sides of this equation by (x+1) to get:
5*(x+2) = 7*(x+1)
simplify by distributing the multiplication to get:
5x+10 = 7x+7
subtract 5x from both sides of the equation and subtract 7 from both sides of the equation to get:
10-7 = 7x-5x
combine like terms to get:
3 = 2x
solve for x to get x = 2/3.
that's your solution.
confirm by replacing x in the original equation with 2/3 to confirm that the original equation is true with that value of x.
the following tutorials contain good info on logs.
read the tutorials and do the exercises.
that will help.
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/index.htm
here's more from a different source.
http://www.themathpage.com/aprecalc/logarithms.htm
lot's of stuff on the web.
it just takes a little looking to get the one that makes the most sense to you.
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