SOLUTION: Solve the following logarithmic equation. Check all solutions. (Enter solutions from smallest to largest). 1/2log(4x+5)=log(x)

Question 371939: Solve the following logarithmic equation. Check all solutions. (Enter solutions from smallest to largest).
1/2log(4x+5)=log(x)
Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
Solve the following logarithmic equation. Check all solutions. (Enter solutions from smallest to largest).
1/2log(4x+5)=log(x)

(1/2)log(4x + 5) = log(x)
base b when not specified is assumed to be 10
log(4x + 5) = 2log(x) (multiplied both sides by 2)
logarithmic rule: nlogb(m) = logb(m^n)
log(4x + 5) = log(x^2)
4x + 5 = x^2 (what is in parenthesis must equal)
-x^2 + 4x + 5 = 0
x^2 - 4x - 5 = 0 (divided both sides by -1)
(x - 5)(x + 1) = 0 by FOIL this is x^2 + x - 5x - 5 or x^2 - 4x - 5
x = -1 or x = 5
x can not be -1, 10 to the somthing can not equal - 1
the solution is x = 5
check:
(1/2)log(4(5) + 5) = log(5)
log(20 + 5) = 2log(5)
log(25) = log(5^2)
log(25) = log(25), yes

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