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

1 Answer
May 23, 2018

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