Originally Posted by

**charlesrussell** Hi,

I am doing a review on logarithms. When I reached my last question's solution I found something strange.

Question: Solve, Ln(y-1)=1+Ln(3y+2)

The solution gives:

Step 1. Ln(y-1)-Ln(3y+2)=1

Ln((y-1)/(3y+2))=1

Step 2. ** e**^( Ln((y-1)/(3y+2))=**e**^1

(y-1)/(3y+2)=**e**

The solution then goes on:

y-1=**e**(3y+2)=3**e***y+2**e**

(1-3**e**)y=1+2**e**

Finally,

y=(1+2**e**)/(1+3**e**)=-0.8996

I found no solution and after graphing saw that there could be no solution for real numbers.

Can you tell me what's wrong here and what does **e** mean without an index?

How does **e** become -0.404273?

Or is there something I have failed to recognise?