Question

How to solve ln (1+x)= 1+ ln x ?

Answer 1

`x=1/(e-1)~~0.582`

Explanation:

Step 1
First, we must move all terms to one side.
`ln(1+x)-1-lnx=0`

Step 2
We can now further simplify using the quotient rule.
`ln((1+x)/x)-1=0`

Step 3
We can now combine like terms to reduce the equation.
`ln(1/x+1)-1=0`

Step 4
Next, we begin to isolate the variable, `x`, by moving everything else to the other side.
`ln(1/x+1)=1`

Step 5
We then use the natural logarithm.
`1/x+1=e`

Step 6
We continue to isolate `x`.
`1/x=e-1`

Step 7
Finally, we simplify and determine our final answer.
`x=1/(e-1)~~0.582`