How do you solve ln(x+1)-lnx=5?

2 Answers
Jun 9, 2017

See below.

Explanation:

When we subtract two natural logs (or two logs in general), we divide the expressions on the inside.

ln(x+1)-lnx=5

ln((x+1)/x)=5

e^5=(x+1)/x

xe^5=x+1

xe^5-x=1

x(e^5-1)=1

x=1/(e^5-1)

Jun 9, 2017

I got: x=1/(e^5-1)=0.006783

Explanation:

We can use a property of logs:

logx-logy=log(x/y)

and write:

ln((x+1)/x)=5

use the definition of (natural) log:

(x+1)/x=e^5

rearrange:

x+1=xe^5

x(e^5-1)=1

x=1/(e^5-1)=0.006783