SOLUTION: How do you find log(x+21)+logx=2?

Algebra.Com
Question 613455: How do you find log(x+21)+logx=2?
Answer by radh(108)   (Show Source): You can put this solution on YOUR website!
Combine using the product rule of logarithms.

Let both sides have a base of 10.

Remember that log is assumed to be 10 if there's no number specified. Because we made the equation have a base of 10, we can then cancel out the logs.

Multiply x by each term inside the parentheses.

Square 10.

Move 100 to the other side.

Factor.

Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)
In order to factor , first we need to ask ourselves: What two numbers multiply to -100 and add to 21? Lets find out by listing all of the possible factors of -100


Factors:

1,2,4,5,10,20,25,50,100,

-1,-2,-4,-5,-10,-20,-25,-50,-100,List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to -100.

(-1)*(100)=-100

(-2)*(50)=-100

(-4)*(25)=-100

(-5)*(20)=-100

(-10)*(10)=-100

Now which of these pairs add to 21? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 21

||||||||||
First Number|Second Number|Sum
1|-100|1+(-100)=-99
2|-50|2+(-50)=-48
4|-25|4+(-25)=-21
5|-20|5+(-20)=-15
10|-10|10+(-10)=0
-1|100|(-1)+100=99
-2|50|(-2)+50=48
-4|25|(-4)+25=21
-5|20|(-5)+20=15
-10|10|(-10)+10=0
We can see from the table that -4 and 25 add to 21.So the two numbers that multiply to -100 and add to 21 are: -4 and 25 Now we substitute these numbers into a and b of the general equation of a product of linear factors which is: substitute a=-4 and b=25 So the equation becomes: (x-4)(x+25) Notice that if we foil (x-4)(x+25) we get the quadratic again


Set each of the factors equal to 0.
,

Simplify.
,

Here is the final answer:
x=-25,4

:)

RELATED QUESTIONS

How do you solve... (answered by rothauserc)
logx+log(x+21)=2 (answered by erica65404,Alan3354)
how do you solve... (answered by Theo)
How do I solve these equations? a) {{{log(6,(x+5))+ log(6,x)=2}}} b) {{{logx=log... (answered by josmiceli)
How do I solve the following problems logx + log1.4 =2 lnx - ln1.4 =2 and... (answered by josmiceli)
log(3) 21 - log(3) 7 = log(3)Y what and how do you find the Y? (answered by jim_thompson5910,stanbon)
How do you solve this for x exactly?... (answered by ewatrrr)
Can you help me with some questions to help me understand how to do it? log5 7x=2... (answered by ikleyn,josmiceli)
log(x+2)=(logx)+... (answered by edjones)