solver for x: ln(x+3)-ln(x)=2ln(2)?

Question

answer should be x=1

Answer 1

ln(x+3)-ln(x)=2ln(2) using quotient rule lnA-lnB= ln(A/B)
and lna^n= nlna
ln([x+3]/x)= ln2^2
ln([x+3]/x)= ln4
since they have the same base so
(x+3)/x = 4
crossed multiply
x+3= 4x
subtract x both sides
3 = 3x
divide 3 both sides
x = 1

Answer 2

One convenient property of logarithms is that
ln(A) - ln(B) = ln(A/B), so applying this you can reduce the equation to
ln( (x+3)/x ) = 2ln(2)
ln( 1+ (3/x)) =2ln(2)
ln(1+(3/x))=ln(4)
because a*ln(b) = ln(b^a), 2^2 =4
Then
1+(3/x) = 4
3/x =3
x=1

Answer 3

Hey there!

Here's the answer.

ln(x+3)-ln(x)=2ln(2) --> Write the problem.
ln((x+3)/x)=2ln(2) --> Use the property, ln(m)-ln(n)=ln(m/n), on the left side of the equation.
ln((x+3)/x)=ln(4) --> Use the property, nln(m)=ln(m^n), on the right side of the equation.
(x+3)/x=4 --> Use one-to-one property of logarithms i.e. if ln(a)=ln(b), then a=b.
x+3=4x --> Multiply x on both sides of the equation.
3=3x --> Subtract x on both sides of the equation.
1=x --> Divide 1 on both sides of the equation.
x=1 Use symmetric property of equality i.e. if a=b, then b=a.

So the answer is x=1.

Hope it helps!

Answer 4

ln(x+3)-ln(x)=2ln(2)
ln((x+3)/x)=ln(4)
(x+3)/x = 4
x+3 = 4x
3x = 3
x = 1

Answer 5

rewrite as ln[(x+3)/x]=ln(2^2)
take exp of both sides to get
(x+3)/x=4
x+3=4x
3x=3
x=1

Answer 6

ln [ (x + 3) / x ] = ln (2 ²)
(x + 3) / x = 4
x + 3 = 4x
3 = 4x - x
3x = 3
x = 1

Answer 7

ln(x+3)-ln(x)=2ln(2)
ln[(x+3)/x]=ln(4)
[(x+3/x)]=(4)
x+3=4x
3x=3
x=1,ANS