SOLUTION: Solve for x log(base 4) x + log(base 4) (x-2) = 1

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Question 1015407: Solve for x
log(base 4) x + log(base 4) (x-2) = 1
Found 3 solutions by josmiceli, josgarithmetic, ikleyn:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
use the substitution:





Complete the square



Take the square root of both sides


and also:


------------------
check:




OK
You can check the other answer
Answer by josgarithmetic(39623)   (Show Source): You can put this solution on YOUR website!
Pure text , log(4,x)+log(4,(x-2))=1

Adding the triple-braces rendering tags,






----not factorable






Answer by ikleyn(52835)   (Show Source): You can put this solution on YOUR website!
.
Solve for x
log(base 4) x + log(base 4) (x-2) = 1
----------------------------------------- 

It is equivalent to

x*(x-2) = 4,     (1)

 = ,

 =  =  = .

So, the solutions of the equation (1) are  and .

Only positive value x =  satisfies the original equation.


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