Question

How do you solve `ln(4x+1)=ln(2x+5)`?

Answer 1

`x = 2`

Explanation:

Remembering that taking the exponential of a natural logarithm gets rid of the natural logarithm, we can apply it in this case to have a simpler equation, giving us

`cancel(e)^(cancel(ln)(4x+1)) = cancel(e)^(cancel(ln)(2x+5))`

`4x+1 = 2x+5`

Now, subtracting `2x` from both sides yields

`2x+1 = 5`

Subtracting `1` from both sides gives us

`2x = 4`, so `x = 2`