Solve the equation. \ln x=1+\ln (x+1)

geduiwelh

geduiwelh

Answered question

2021-09-19

Solve the equation.
lnx=1+ln(x+1)

Answer & Explanation

i1ziZ

i1ziZ

Skilled2021-09-20Added 92 answers

Step 1
Given :
The equation is lnx=1+ln(x+1)
To solve the given equation.
Step 2
lnx=1+ln(x+1)
lnxln(x+1)=1
ln(xx+1)=1 (since lnalnb=ln(ab))
Taking exponential on both sides,
eln(xx+1)=e1
xx+1=e
x=(x+1)e
x=xe+e
x(1e)=e
x=e1e
Therefore, the solution of the equation lnx=1+ln(x+1) is x=e1e.

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