SOLUTION: Solve problem exactly ln (x + 1) = ln (3x + 1)- ln x

Question 4558: Solve problem exactly
ln (x + 1) = ln (3x + 1)- ln x
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!

By the second law of logarithms,

Now, since there are ln s on both sides of the equation, raise both sides as a power of e:

Multiply both sides of this equation by x

Set equal to zero:

Solve by quadratic formula, where and a= 1, b= -2, c = -1.

Factor the numerator, so you can reduce the fraction:

or

However, the second solution is a negative number, which is NOT allowed in the last ln expression. So the only solution is

R^2 at SCC
RELATED QUESTIONS
ln(x+1)=ln(3x+1) - lnx solve... (answered by venugopalramana)

solve:... (answered by dabanfield)

Solve for x:... (answered by josgarithmetic)

SOLVE FOR X ln(ln x) =... (answered by vleith)

ln x + ln (x+1)= ln... (answered by stanbon)

Solve... (answered by stanbon)

Solve ln(3x+4)=... (answered by prateekagrawal)

how do I solve... (answered by stanbon)

Solve: log base 4 (X) + Log base 8 (x) = 1 ln X/ln 4 + ln X/ln 8=1 2 ln X/2 ln 4 + ln... (answered by Fombitz)