Answer :
First we will find which values x should not exist.
Log(x -21)
Well,
x - 21 > 0
Then,
x > 21
_______________
Now, we let's to the question
First,
Rewrite 2 = Log 100
Then,
Log (x -21) = Log 100 - Log(x)
Use the property:
Log(a) - Log(b) = Log( a / b)
Then,
Log( 100) - Log( x) = Log(100/x)
So us wiil stay:
Log(x - 21) = Log(100/x)
Now cancel the Logs...
x - 21 = 100/x
Isolating x to the letf side:
x( x - 21) = 100
Applying the distributive on the member firft:
x^2 - 21x = 100
Passing 100 to the left side of equation us will have:
x^2 - 21x - 100 = 0
Now we've a equation of baskara:
Where,
a = 1
b = -21
c = -100
So follow :
Delta = b^2 -4ac
Delta = (-21)^2 -4.(1).(-100)
Delta = 441 + 400
Delta = 841
As x = [ -b +/- √( Delta) ] /2a
Then,
x = [ -(-21) +/- √(841) ]/2.(1)
x = [ 21 +/- 29 ]/2
______________
1:
x = (21 - 29)/2
x = -4
Or
x = (21 + 29)/2
x = 25
_____________
As X > 21
Then,
x = - 4 not exist.
Just x = 25 would be the answer.
Log(x -21)
Well,
x - 21 > 0
Then,
x > 21
_______________
Now, we let's to the question
First,
Rewrite 2 = Log 100
Then,
Log (x -21) = Log 100 - Log(x)
Use the property:
Log(a) - Log(b) = Log( a / b)
Then,
Log( 100) - Log( x) = Log(100/x)
So us wiil stay:
Log(x - 21) = Log(100/x)
Now cancel the Logs...
x - 21 = 100/x
Isolating x to the letf side:
x( x - 21) = 100
Applying the distributive on the member firft:
x^2 - 21x = 100
Passing 100 to the left side of equation us will have:
x^2 - 21x - 100 = 0
Now we've a equation of baskara:
Where,
a = 1
b = -21
c = -100
So follow :
Delta = b^2 -4ac
Delta = (-21)^2 -4.(1).(-100)
Delta = 441 + 400
Delta = 841
As x = [ -b +/- √( Delta) ] /2a
Then,
x = [ -(-21) +/- √(841) ]/2.(1)
x = [ 21 +/- 29 ]/2
______________
1:
x = (21 - 29)/2
x = -4
Or
x = (21 + 29)/2
x = 25
_____________
As X > 21
Then,
x = - 4 not exist.
Just x = 25 would be the answer.