Solve for x: ln (2x-1)=ln (x+3)?

Question

The answer should be x=4... It's been a while since I've worked with logarithms.. So a quick refreshment would be fantastic.

Answer 1

If ln A = ln B then A = B
2x - 1 = x + 3
x = 4

Answer 2

Since the ln has been taken on both sides:
ln (2x-1)=ln (x+3) === (2x -1) = (x + 3)
Solving for x
2x - x = 1 + 3
x = 4

Answer 3

Hey there!

Here's the answer.

ln(2x-1)=ln(x+3) --> Write the problem.
2x-1=x+3 --> Use one-to-one property of logarithms i.e. if ln(a)=ln(b), then a=b.
x-1=3 --> Subtract x on both sides of the equation.
x=4 Add 1 on both sides of the equation.

So the answer is x=4.

Hope it helps!

Answer 4

take out ln, we can get 2x-1 = x +3 so x =4

Answer 5

ln(2x - 1) = ln (x + 3)
-> ln(2x - 1) - ln (x + 3) = 0
-> ln[(2x - 1)/(x + 3)] = 0 = ln 1
-> (2x - 1)/(x + 3) = 1
-> 2x - 1 = x + 3
-> x = 4