Question

Use the properties of logarithms to evaluate the expression Ln e^sqrt(7)

I know the answer is 1, but I don't know why it's 1. Can someone explain?

Answer 1

it's sqrt7

Answer 2

Here is an approach you could take.
A rule of logarithms:\[\large \color{royalblue}{\log(a^b)=b\cdot \log(a)}\]

Answer 3

Understand how we can apply this rule?
\[\Large \ln\left(e^{\sqrt7}\right)=?\]

Answer 4

So \[Ln(e^\sqrt{7}) = Log _{e}e ^{\sqrt{7}} = \sqrt{7} * Log _{e}e\]
I don't quite get how this equals 1. I'm not supposed to use a calculator to understand it.

Answer 5

Ok good that's our first step.

Hmm if you can't use a calculator then you need to try and remember some things about logs.