# Thread: Why is 10^lg 5=5 and e^ln5=5, etc?

1. ## Why is 10^lg 5=5 and e^ln5=5, etc?

Why is

$(10^\lg5)=5$
$(e^\ln5)=5$

so on and so forth?

2. Because the notation $\log$ is being used to represent the logarithm of base $10$, and $\ln$ is being used to represent the logarithm of base $e$.

3. Originally Posted by Prove It
Because the notation $\log$ is being used to represent the logarithm of base $10$, and $\ln$ is being used to represent the logarithm of base $e$.
Can you break it down further so that I can digest that information?

4. Thread closed. I dunno why i have double thread. Moderator can delete for me and transfer this reply over to the other?

5. You should know that exponentials undo logarithms and vice versa.

So $a^{\log_a{x}} = x$ and $\log_a{(a^x)} = x$.

In your first case, you're using $\lg$ to represent $\log_{10}$ and $\ln$ to represent $\log_e$.

6. Originally Posted by stupidguy
Thread closed. I dunno why i have double thread. Moderator can delete for me and transfer this reply over to the other?