SOLUTION: solve log x+log(x+21)=2

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Question 607150: solve log x+log(x+21)=2
Found 4 solutions by ewatrrr, jim_thompson5910, Gogonati, lawdej:
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!

Hi,
log x+log(x+21)=2
log x(x+21) = 2
10^2 = x^2 + 21x
x^2 + 21x-100 = 0
Factoring***
(x+25(x-4) = 0
(x+25) = 0, x =
(x-4) = 0, x = 4
Using FOIL to check our Factoring***
F First terms x^2
O Outside terms -4x
I Inside terms +25x
L Last terms -100

Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
log(x) + log(x+21) = 2

log(x(x+21)) = 2

log(x^2+21x) = 2

x^2+21x = 10^2

x^2+21x = 100

x^2+21x-100 = 0

(x-4)(x+25) = 0

x-4=0 or x+25=0

x=4 or x=-25

Throw out the negative solution since you can't take the log of a negative number.

So the only solution is

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Answer by Gogonati(855)   (Show Source):
You can put this solution on YOUR website!

The solution set is: {4}
We extract -25 because the neg log does not exist.

Answer by lawdej(58)   (Show Source):
You can put this solution on YOUR website!
log x+log(x+21)=2
first determine domain
domain=x>0 and x>-21=x>0
log(x*(x+21))=2
log(x^2+21x)=2
x^2+21x=10^2
x^2+21x=100
x^2+21x-100=0
x^2-4x+25x-100=0
x(x-4)+25(x-4)=0
(x+25)+(x-4)=0
(x+25)=0 or(x-4)=0
x=-25 or x=4
or
use quadratic formula
x^2+21x-100=0
x=(-21+or-square root of (441+400))/2
x=(-21+or-square root of (841))/2
x=(-21+or- 29)/2
x=(-21+29)/2 or x=(-21-29)/2
x=8/4 or x=-50/2
x=4 or x=-25
but the solution is only x=4 since -25 is not in the domain
(lawdej@yahoo.com)