# Thread: simplification of a logarithm

1. ## simplification of a logarithm

Original problem is $\displaystyle 2e^{3x+5}=6$. Ive gotten it to $\displaystyle ln e^{3x+5}=ln3$. Ordinarily I would change the 3x+5 into the coefficient of lne and go from there but in the example problem Im looking at they simply remove the ln e. Basically this is what they did: They took $\displaystyle ln e^{3x+5}=ln3$ and simplified it to $\displaystyle 3x+5=ln 3$. So my question is what rule or property did they use to get rid of the LN e?

2. They combined two rules. First, they converted the exponent to a coefficient, like you were going to do. Then, they used the rule $\displaystyle \ln{e} = 1$. Multiplication by 1 doesn't change anything so you are left with just the coefficient.

Original problem is $\displaystyle 2e^{3x+5}=6$. Ive gotten it to $\displaystyle ln e^{3x+5}=ln3$. Ordinarily I would change the 3x+5 into the coefficient of lne and go from there but in the example problem Im looking at they simply remove the ln e. Basically this is what they did: They took $\displaystyle ln e^{3x+5}=ln3$ and simplified it to $\displaystyle 3x+5=ln 3$. So my question is what rule or property did they use to get rid of the LN e?