SOLUTION: 1+(4/3)log(base x-3) 4 = 11/3 base= x-3 this is soo confusing, i spent so long but i just don't get it =(. please help !

Question 489711: 1+(4/3)log(base x-3) 4 = 11/3
base= x-3
this is soo confusing, i spent so long but i just don't get it =(. please help !
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
1+log(basex-3)(4) =
Simplify by just using basic algebra
subtract 1 from both sides
log(basex-3)(4) =
:
log(basex-3)(4) =
:
multiply both sides by 3
4log(base x-3)(4) = 8
:
divide both sides by 4
log(base x-3)(4) = 2
:
Write the exponent equiv of logs
(x-3)^2 = 4
:
FOIL(x-3)(x-3)
x^2 - 6x + 9 = 4
:
Subtract 4 from both sides
x^2 - 6x + 5 = 0
:
Factors to
(x-1)(x-5) = 0
:
Two solutions
x = 1, not a solution, can't have a base of a neg number
x = 5, this is the valid solution
:
:
see if it works in the original problem
1+log(base5-3)(4) =
1+log(base2)(4) =
simplify using the same rules we did above.
log(base2)(4) =
log(base2)(4) =
4log(base2)(4) = 8
log(base2)(4^4) = 8
log(base2)(256) = 8
exponent equiv
2^8 = 256, equality reigns

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