Solve log(5x+6)/2=logx?

Answer 1

if by this you mean

(log(5x + 6))/2 = log(x)

log(5x + 6) = 2log(x)
log(5x + 6) = log(x^2)
5x + 6 = x^2
x^2 - 5x - 6 = 0
(x - 6)(x + 1) = 0
x = 6 or -1

since you can't have a log(-1), since that would make the problem undefined.

ANS : x = 6

Answer 2

log[(5x+6)/2]=logx (x must be possitive)
<=> (5x + 6)/2 = x <=> x = -2 ( unacceptable )

[log(5x+6)]/2=logx (x must be possitive)
<=>log(5x+6)=2logx
<=> log(5x+6)=log(x^2)
<=> x^2 - 5x - 6 = 0 <=> x = -1(unaccepted) or x = 6 (accepted)

Answer 3

[log(5x+6)]/2=logx
then
log((5x+6)^0.5)=logx
(5x+6)^0.5=x
5x+6=x^2
x^2-5x - 6=0
(x+1)(x-6)=0
x=-1 or x=6
-1 doesn't work with logs, so answer is 6

Answer 4

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