# Thread: [SOLVED] Find the domain and range

1. ## [SOLVED] Find the domain and range

What is the domain and range of this function?
ln(e^(2x-1))

i dont know if my answer is right but i got x is not 1/2
and y = real numbers??

does this graph look like a normal log one?

i plug in numbers and i keep getting a diagonal line?

2. Originally Posted by NeedHelp18
What is the domain and range of this function?
ln(e^(2x-1))

i dont know if my answer is right but i got x is not 1/2
and y = real numbers??
When $\displaystyle x=\frac12,$ you have $\displaystyle \ln\left(e^{2x-1}\right)=\ln e^0=\ln1=0\text.$ Why are you excluding that from the domain?

does this graph look like a normal log one?

i plug in numbers and i keep getting a diagonal line?
What is $\displaystyle \ln e^n?$ Or in general, $\displaystyle \log_aa^n?$ Hint: the natural logarithm and the natural exponential function are inverses of each other.

3. i am lost now

so what would be the domain?

all real numbers?

and is my range correct?

4. Originally Posted by NeedHelp18
i am lost now

so what would be the domain?

all real numbers?
Yes. $\displaystyle e^x$ is defined for all real $\displaystyle x,$ its range is $\displaystyle (0,\infty),$ and $\displaystyle \ln x$ is defined for those values.

and is my range correct?
Yes. The range of $\displaystyle e^x$ covers the entire domain of the natural logarithmic function and the range of the natural logarithmic function is $\displaystyle (-\infty,\infty)\text.$